Exhibit 5.1

November 13, 2023

Eastern Bankshares, Inc.

265 Franklin Street

Boston, Massachusetts 02110

Re: Securities Being Registered under Registration Statement on Form S-4

Ladies and Gentlemen,

We acted as counsel in connection with your filing of a Registration Statement on Form S-4 (as amended or supplemented, the “Registration Statement”) filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of up to 39,620,000 shares of Common Stock, $0.01 par value per share (the “Shares”), of Eastern Bankshares, Inc., a Massachusetts corporation (the “Company”). The Shares are to be issued by the Company pursuant to the Agreement and Plan of Merger (the “Merger Agreement”), dated as of September 19, 2023, by and among the Company, Cambridge Bancorp, Citadel MS 2023, Inc., Eastern Bank and Cambridge Trust Company, which has been filed as Annex A to the Joint Proxy Statement/Prospectus forming part of the Registration Statement.

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Massachusetts Business Corporation Act (which includes reported judicial decisions interpreting the Massachusetts Business Corporation Act).

Based on the foregoing, we are of the opinion that, as of the Effective Time of the Merger (as each term is the defined in the Merger Agreement), the Shares will be duly authorized and, upon issuance and delivery in accordance with the terms of the Merger Agreement, the Shares will be validly issued, fully paid and non-assessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Nutter, McClennen & Fish, LLP

Nutter, McClennen & Fish, LLP