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 Annual Report on Form 10-K of Arthur J. Gallagher & Co. for the twelve month period ended December 31, 2023 (the “Form 10-K”) 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-K fairly presents, in all material respects, the financial condition and results of operations of Arthur J. Gallagher & Co. and its subsidiaries.

Date: February 9, 2024