Exhibit 32.1

CERTIFICATION

PURSUANT TO 18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906 OF THE

SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Eastern Bankshares, Inc. (the “Company”) for the period ending June 30, 2024 (the “Report”), as filed with the Securities and Exchange Commission on the date hereof, the undersigned hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the undersigned’s best knowledge and belief:

(a)the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (“Exchange Act”); and

(b)the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: August 7, 2024
	Eastern Bankshares, Inc.
	(“Company”)
	/s/ Robert F. Rivers
	Robert F. Rivers Executive Chair (Principal Executive Officer)

This certification accompanies this Quarterly Report on Form 10-Q pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by such Act, be deemed filed by the Company for purposes of Section 18 of the Exchange Act. Such certification will not be deemed to be incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Exchange Act, except to the extent that the Company specifically incorporates it by reference.

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company.