Exhibit 32.1

Section 1350 Certification of Chief Executive Officer

I, J. Patrick Gallagher, Jr., the chief executive officer of Arthur J. Gallagher & Co., certify that (i) the Quarterly Report on Form 10-Q of Arthur J. Gallagher & Co. for the quarterly period ended March 31, 2024 (the “Form 10‑Q”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of Arthur J. Gallagher & Co. and its subsidiaries.

Date: May 1, 2024

A signed original of this written statement required by 18 U.S.C. Section 1350 has been provided to Arthur J. Gallagher & Co. and will be retained by Arthur J. Gallagher & Co. and furnished to the Securities Exchange Commission or its staff upon request.