1 EDGAR NEXT & SECTION 16 REPORTING – POWER OF ATTORNEY Know all by these presents, that I do here appoint each of Roy E. Halyama, Matthew W. Rucker, Patrick “Kip” Huffman, Kirtan Parikh, and Zayne R. Tweed, each acting singly, and with full power of substitution, re-substitution, and delegation, the undersigned’s true and lawful attorney-in-fact (each of such persons and their substitutes and delegees being referred to herein as the “Attorney-in-Fact”), with full power to act for the undersigned and in the undersigned’s name, place and stead, in the undersigned’s capacity as an officer, director, or stockholder of Burke & Herbert Financial Services Corp. (the “Company”), to: 1. Take such actions as may be necessary or appropriate to enable the undersigned to submit and file forms, schedules and other documents with the U.S. Securities and Exchange Commission (“SEC”) utilizing the SEC’s Electronic Data Gathering and Retrieval (“EDGAR”) system, which actions may include (a) enrolling the undersigned in EDGAR Next and (b) preparing, executing and submitting to the SEC a Form ID, amendments thereto, and such other documents and information as may be necessary or appropriate to obtain codes and passwords enabling the undersigned to make filings and submissions utilizing the EDGAR system; 2. Prepare and execute any and all forms, schedules and other documents (including any amendments thereto) the undersigned is required to file with the SEC, or which the Attorney- in-Fact considers it advisable for the undersigned to file with the SEC, under Section 13 or Section 16 of the Securities Exchange Act of 1934 or any rule or regulation thereunder, or under Rule 144 under the Securities Act of 1933 (“Rule 144”), including Forms 3, 4 and 5, Schedules 13D and 13G, and Forms 144 (all such forms, schedules and other documents being referred to herein as “SEC Filings”); 3. Submit and file SEC Filings with the SEC utilizing the EDGAR system or cause them to be submitted and filed by a person appointed under paragraph 5 below; 4. File, submit or otherwise deliver SEC Filings to any securities exchange on which the Company’s securities may be listed or traded; 5. Act as an account administrator for the undersigned’s EDGAR account, including: (a) appoint, remove and replace account administrators, account users, technical administrators and delegated entities; (b) maintain the security of the undersigned’s EDGAR account, including modification of access codes; (c) maintain, modify and certify the accuracy of information on the undersigned’s EDGAR account dashboard; (d) act as the EDGAR point of contact with respect to the undersigned’s EDGAR account; and (e) any other actions contemplated by Rule 10 of Regulation S-T with respect to account administrators; 6. Cause the Company to accept a delegation of authority from any of the undersigned’s EDGAR account administrators and, pursuant to that delegation, authorize the Company’s EDGAR account administrators to appoint, remove or replace users for the undersigned’s EDGAR account; and 7. Obtain, as the undersigned’s representative and on the undersigned’s behalf, information regarding transactions in the Company’s equity securities from any third party, including the Company and any brokers, dealers, employee benefit plan administrators and trustees, and the

2 undersigned hereby authorizes any such third party to release any such information to the Attorney-in-Fact. 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) Any documents prepared or executed by the Attorney-in-Fact on behalf of the undersigned pursuant to this Power of Attorney will be in such form and will contain such information as the Attorney-in-Fact, in his or her discretion, deems necessary or desirable; (c) Neither the Company nor the Attorney-in-Fact assumes any liability for the undersigned’s responsibility to comply with the requirements of Section 13 or Section 16 of the Exchange Act or Rule 144, 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 (d) This Power of Attorney does not relieve the undersigned from responsibility for compliance with the undersigned’s obligations under Section 13 or Section 16 of the Exchange Act, including, without limitation, the reporting requirements under Section 13 or Section 16 of the Exchange Act. The undersigned hereby grants to the Attorney-in-Fact full power and authority to do and perform each and every act and thing requisite, necessary or advisable to be done in connection with the foregoing, as fully, to all intents and purposes, as the undersigned might or could do in person, hereby ratifying and confirming all that the Attorney-in-Fact, or his or her substitute or substitutes, shall lawfully do or cause to be done by authority of this Power of Attorney. This Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file Forms 4 or 5 or Schedules 13D or 13G or Forms 144 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 Attorney-in-Fact. This Power of Attorney revokes all previous powers of attorney with respect to the subject matter of this Power of Attorney. [remainder of page intentionally blank; signature page to follow]

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of this ____ day of June 2025 . _/;J a:7 J t,?ad/ Signatur t~rv L ~ 1-lr~n k' ( Print Naq/e: Gary L. Hinkle COMMONWEALTH OF VIRGINIA CITY OF ALEXANDRIA The undersigned, a notary public in and for the above cou~t and state, hereby certifies that the foregoing instrument was acknowledged before me on this -t'\.. day of June 2025 by the above-named signatory. IN WITNESS WHEREOF, I have hereunto set my hand and official seal. ~ J ~ Name: Notary Public -it- to, '7/,,J"& {;U.,., 0 J w-1-..---.,,,..,, ,._-<. My Commission Expires: 26th

HINKLE GARY L 4