Exhibit 24 POWER OF ATTORNEY The undersigned hereby constitutes and appoints each of Brian Sondey, John Burns and Carla Heiss, or any of them acting singly, and with full power of substitution, as the undersigned's true and lawful attorney-in-fact (each of such persons and their substitutes being referred to as the “Attorney-in-Fact”), with full power to act for the undersigned and in the undersigned’s name, place and stead, to: (1) Prepare, execute and submit to the U.S. Securities and Exchange Commission (the "SEC"), a Form ID, including amendments thereto, and any other documents necessary or appropriate to obtain codes and passwords enabling the undersigned to make electronic filings with the SEC of reports required or considered by the Attorney-in-Fact to be advisable under Section 16(a) of the Securities Exchange Act of 1934 (the “Exchange Act”) or any rule or regulation of the SEC; (2) Prepare, execute submit to the SEC, and to other entities as required, all of the Forms 3, 4 and 5, including any amendments thereto, to be filed with respect to the ownership of, or transactions in, securities of Triton International Limited (the “Company”) beneficially owned by the undersigned; (3) Obtain, as the undersigned’s representative and on the undersigned’s behalf, information regarding transactions in the Company’s securities from any third party, including the company and any brokers, dealers, employee benefit plan administrators and trustees, and the undersigned hereby authorizes any such third party to release any such information to the Attorney-in-Fact. (4) do and perform any and all acts for and on behalf of the undersigned that may be necessary or desirable to complete and execute any such Form 3, 4 or 5, complete and execute any amendment or amendments thereto, and timely file such form with the SEC and as otherwise required; and (5) take any other action of any type whatsoever in connection with the foregoing which, in the opinion of such Attorney-in-Fact, may be of benefit to, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such Attorney-in-Fact on behalf of the undersigned pursuant to this Power of Attorney will be in such form and will contain such terms and conditions as such Attorney-in-Fact may approve in such Attorney-in- Fact's discretion. The undersigned acknowledges that: a. This Power of Attorney authorizes, but does not require, the Attorney-in-Fact to act in his or her discretion on information provided to such Attorney-in-Fact without independent verification of such information; b. Neither the Company nor the Attorney-in-Fact assumes any liability for the undersigned’s responsibility to comply with the requirements of Section 16 of the Exchange Act, any liability of the undersigned for any failure to comply with

such requirements, or any liability of the undersigned for disgorgement of profits under Section 16(b) of the Exchange Act; and c. This Power of Attorney does not relieve the undersigned from any responsibility for compliance with the undersigned’s obligations under Section 16 of the Exchange Act, including, without limitation, the reporting requirements under Section 16 of the Exchange Act. The undersigned hereby grants to each such Attorney-in-Fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary, or advisable to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do in person, with full power of substitution or revocation, hereby ratifying and confirming all that such Attorney-in-Fact, or such Attorney-in- Fact's substitute or substitutes, will lawfully do or cause to be done by virtue of this Power of Attorney and the rights and powers herein granted. This Power of Attorney will remain in full force and effect until the undersigned is no longer required to file Forms 3, 4, and 5 with respect to the undersigned's holdings of and transactions in securities of the Company, unless earlier revoked by the undersigned in a signed writing delivered to the foregoing Attorneys-in-Fact. This Power of Attorney revokes all previous powers of attorney with respect to the subject matter of this Power of Attorney. *** IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed this 12th day of February, 2020. _/s/ Robert L. Rosner_____________ Signature _Robert L. Rosner________________ Print Name

Rosner Robert L. 4