Exhibit 10.3

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT (as it may be amended from time to time and including all exhibits referenced herein, this “Agreement”), dated as of [], 2021, is entered into by and between Peridot Acquisition Corp. III, a Cayman Islands exempted company (the “Company”) and Peridot Acquisition Sponsor III, LLC, a Delaware limited liability company (the “Purchaser”).

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one of the Company’s Class A ordinary shares, par value $0.0001 per share (the “Shares”), and one-[ ] of one redeemable warrant, each whole warrant entitling the holder thereof to purchase one Share at an exercise price of $11.50 per Share, as set forth in the Company’s registration statement on Form S-l (File Number 333-[ ]) (the “Registration Statement”), filed with the U.S. Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”).

WHEREAS, the Purchaser has agreed to purchase an aggregate of [ ] redeemable warrants (or up to [] warrants if the underwriters in the Public Offering exercise their option to purchase additional units in full (such option, the “Over-allotment Option”) and such warrants, the “Private Placement Warrants”). Each whole Private Placement Warrant entitles the holder thereof to purchase one Share at an exercise price of $11.50 per Share.

NOW THEREFORE, in consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows:

AGREEMENT

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement Warrants.

A.Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement Warrants to the Purchaser.

B.Purchase and Sale of the Private Placement Warrants.

(i)On the date that is one (1) business day prior to the date of the consummation of the Public Offering (the “IPO Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, [ ] Private Placement Warrants at a price of $[] per Private Placement Warrant for an aggregate purchase price of $[ ] (the “Purchase Price”). The Purchaser shall pay the Purchase Price by wire transfer of immediately available funds in the following amounts: (i) $[ ] to the Company at a financial institution to be chosen by the Company and (ii) $[ ] to the trust account maintained by Continental Stock Transfer & Trust Company, acting as trustee (the “Trust Account”), in each case in accordance with the Company’s wiring instructions. On the IPO Closing Date, subject to the receipt of funds pursuant to the immediately prior sentence, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser, or effect such delivery in book-entry form.

(i)On the date that is one (1) business day prior to the date of the consummation of the Over-allotment Option, if any, in connection with the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (each such date, an “Option Closing Date,” and each Option Closing Date (if any) and the IPO Closing Date being sometimes referred to herein as a “Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to [ ] Private Placement Warrants (or, to the extent the Over-allotment Option is not exercised in full, a lesser number of Private Placement Warrants in proportion to the portion of the Over-allotment Option that is exercised) at a price of $[] per Private Placement Warrant for an aggregate purchase price of up to $[ ] (the “Option Purchase Price”). The Purchaser shall pay the Option Purchase Price in accordance with the Company’s wire instruction by wire transfer of immediately available funds to the Trust Account, at least one (1) business day prior to the Option Closing Date. On the Option Closing Date, subject to the receipt of funds pursuant to the immediately prior sentence, the Company shall, at its option, deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser or effect such delivery in book-entry form.

C.Terms of the Private Placement Warrants.

(i)Each Private Placement Warrant shall have the terms set forth in a Warrant Agreement to be entered into by the Company and a warrant agent on the IPO Closing Date, in connection with the Public Offering (the “Warrant Agreement”).

(ii)On the IPO Closing Date, the Company and the Purchaser shall enter into a registration and shareholder rights agreement (the “Registration and Shareholder Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants and the Shares underlying the Private Placement Warrants.

Section 2. Representations and Warranties of the Company. As a material inducement to the Purchaser to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive each Closing Date) that:

A.Incorporation and Corporate Power. The Company is an exempted company duly incorporated, validly existing and in good standing under the laws of the Cayman Islands and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement.

B.Authorization; No Breach. The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company as of the Closing Date. This Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). Upon issuance in accordance with, and payment pursuant to, the terms of the Warrant Agreement and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding

in equity or law).

(i)The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and will not as of the Closing Date (a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s share capital or assets under, (d) result in a violation of, or (e) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant to the amended and restated memorandum and articles of association of the Company (in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering), or any material law, statute, rule or regulation to which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws.

C.Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, and upon registration in the Company’s register of members, the Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable. On the date of issuance of the Private Placement Warrants, the Shares issuable upon exercise of the Private Placement Warrants shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, and upon registration in the Company’s register of members, the Purchaser will have good title to the Private Placement Warrants and the Shares issuable upon exercise of such Private Placement Warrants, free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state securities laws and (iii) liens, claims or encumbrances imposed due to the actions of the Purchaser.

D.Governmental Consents. No permit, consent, approval or authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions contemplated hereby.

E.Regulation D Qualification. Neither the Company nor, to its actual knowledge, anyof its affiliates, members, officers, directors or beneficial shareholders of 20% or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act.

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter into this Agreement and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) that:

A.Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

B.Authorization; No Breach.

(i)This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law).

(ii)The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser does not and shall not as of each Closing Date (a) conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Purchaser’s equity or assets under, (d) result in a violation of, or (e) require authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant to the Purchaser’s organizational documents in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering, or any material law, statute, rule or regulation to which the Purchaser is subject, or any agreement, instrument, order, judgment or decree to which the Purchaser is subject, except for any filings required after the date hereof under federal or state securities laws.

C.Investment Representations.

(i)The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon such exercise (collectively, the “Securities”), for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof.

(ii)The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act.

(iii)The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities.

(iv)The Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act.

(v)The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials relating to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company. The Purchaser understands that its investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities.

(vi)The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities.

(vii)The Purchaser understands that: (a) the Securities have not been and are not being registered under the Securities Act or any state securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom; (b) except as specifically set forth in the Registration and Shareholder Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder and (c) Rule 144 adopted pursuant to the Securities Act will not be available for resale transactions of Securities prior to a business combination and may not be available for resale transactions of Securities after a business combination.

(viii)The Purchaser has such knowledge and experience in financial and business matters, knows of the high degree of risk associated with investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investment in the Securities.

(ix)The Purchaser understands that the Private Placement Warrants shall bear the legend substantially in the form set forth in the Warrant Agreement.

Section 4. Conditions of the Purchaser’s Obligations. The obligations of the Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A.Representations and Warranties. The representations and warranties of the Company contained in Section 2 hereof shall be true and correct at and as of such Closing Date as though then made.

B.Performance. The Company shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date.

C.No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

D.Warrant Agreement and Registration and Shareholder Rights Agreement. The Company shall have entered into the Warrant Agreement with a warrant agent, substantially in the form attached hereto as Exhibit A, and the Registration and Shareholder Rights Agreement, substantially in the form attached hereto as Exhibit B, in each case on terms satisfactory to the Purchaser.

Section 5.Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A.Representations and Warranties. The representations and warranties of the Purchaser contained in Section 3 hereof shall be true and correct at and as of such Closing Date as though then made.

B.Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by the Purchaser on or before such Closing Date.

C.Corporate Consents. The Company shall have obtained the consent of its board of directors authorizing the execution, delivery and performance of this Agreement and the Warrant Agreement and the issuance and sale of the Private Placement Warrants hereunder.

D.No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

E.Warrant Agreement. The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to the Company.

Section 6. Termination. This Agreement may be terminated at any time after [], 2021, upon the election by either the Company or the Purchaser upon written notice to the other party if the closing of the Public Offering does not occur prior to such date.

Section 7. Survival of Representations and Warrants. All of the representations and warranties contained herein shall survive each Closing Date.

Section 8. Definitions. Terms used but not otherwise defined in this Agreement shall have the meaning assigned to such terms in the Registration Statement.

Section 9. Miscellaneous.

A.Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement, other than assignments by the Purchaser to affiliates thereof (including, without limitation one or more of its members).

B.Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

C.Counterparts. This Agreement may be executed simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement. Signatures to this Agreement transmitted via facsimile or e-mail shall be valid and effective to bind the party so signing.

D.Descriptive Headings; Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of example rather than by limitation.

E.Governing Law. This Agreement shall be deemed to be a contract made under the laws of the State of New York and for all purposes shall be construed in accordance with the internal laws of the State of New York, without giving effect to the conflicts of law principles that would result in the application of the laws of another jurisdiction.

F.Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

[Signature page follows]

IN WITNESS WHEREOF, the parties hereto have executed this Agreement to be effective as of the date first set forth above.

COMPANY:

PERIDOT ACQUISITION CORP. III


By:	___________________________________
Name:	Stephen Wedemeyer
Title:	Chief Financial Officer

PURCHASER:

PERIDOT ACQUISITION SPONSOR III, LLC


By:	___________________________________
Name:	Jeffrey Gilbert
Title:	General Counsel and Corporate Secretary

[Signature page to Private Placement Warrants Purchase Agreement]

EXHIBIT A

Warrant Agreement

[See attached.]

EXHIBIT B

Registration and Shareholder Rights Agreement

[See attached.]

Peridot Acquisition Corp. III S-1