Filed by Provident Bancorp, Inc.

pursuant to Rule 425 under the Securities Act of 1933

and deemed filed pursuant to Rule 14a-12

under the Securities Exchange Act of 1934

Subject Company: Provident Bancorp, Inc.

SEC File No.: 001-39090

Filer’s SEC File No.: 001-39090

Date: June 6, 2025

Dear BankProv customer,

We are writing to let you know that BankProv has entered into a definitive agreement to be acquired by Needham Bank, a commercial bank operating 11 branches throughout Greater Boston and MetroWest. We believe that the merger will provide you with enhanced services through an expanded product set and additional branch locations – without losing your local, high touch customer service.

About Needham Bank

Needham Bank has a strong track record of organic growth and financial strength; it was ranked #20 in S&P Global Marketing Intelligence’s Best Performing Large Community Banks in 2024. Needham Bank has been on the Boston Business Journal’s Top 100 List of Corporate Citizens for several years based on their commitment to giving back. In addition, Needham Bank employees have voted Needham a Boston Globe Top Place to Work 3 times in the last 4 years. Needham’s customer service scores are among the best in our industry.

BankProv and Needham Bank share similar values – both banks believe in being nimble and forward thinking, taking care of customers, communities and employees and investing in technology to remain future-ready. Needham also shares BankProv’s relationship focus, getting to know customers to provide tailored, expert financial advice to help businesses and consumers build for their futures. Together, there will be more resources available to serve you.

What’s Next?

The acquisition is expected to be completed in the fourth quarter of 2025, subject to approval by BankProv shareholders and banking regulators. During this process, we will evaluate each bank’s products and services to make sure we are taking the best from both sides to create an even more robust product line for you. We will also begin planning to convert BankProv accounts to Needham Bank accounts. We both operate on the same core banking platform, so we anticipate that the system conversion will have minimal customer impact.  Until the acquisition is completed in Q4, your accounts and services will remain as they are today, so there is nothing for you to do at this time.

We will keep you up to date on our progress through a resource center at BankProv.com/Needham, where you can also find answers to frequently asked questions (FAQs). When the acquisition gets closer, you will receive a welcome package from Needham Bank with helpful information about Needham Bank accounts and services, and key dates related to the process.

Both of us thank you for your trust in BankProv through the years. We look forward to serving you for many years to come as Needham Bank.

Sincerely,

ADDITIONAL INFORMATION AND WHERE TO FIND IT

In connection with the proposed merger transaction, NB Bancorp, Inc. (“Needham”) intends to file with the SEC a Registration Statement on Form S-4 that will include a Proxy Statement of Provident Bancorp, Inc. (“Provident”) and a Prospectus of Needham (the “proxy statement/prospectus”), as well as other relevant documents concerning the proposed transaction. INVESTORS AND STOCKHOLDERS OF NEEDHAM AND PROVIDENT ARE URGED TO READ THE REGISTRATION STATEMENT AND THE PROXY STATEMENT/PROSPECTUS REGARDING THE TRANSACTION WHEN THEY BECOMES AVAILABLE AND EACH OTHER RELEVANT DOCUMENT FILED WITH THE SEC, AS WELL AS ANY AMENDMENT OR SUPPLEMENT TO THOSE DOCUMENTS, BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Provident will mail the definitive proxy statement/prospectus to its shareholders. Provident shareholders are also urged to carefully review and consider Needham’s and Provident’s public filings with the SEC, including, but not limited to, their respective proxy statements, Annual Reports on Form 10-K, Quarterly Reports on Form 10-Q, and Current Reports on Form 8-K. Copies of the Registration Statement on Form S-4 and of the proxy statement/prospectus and other filings incorporated by reference therein, as well as other filings containing information about Needham and Provident, can be obtained, free of charge, as they become available at the SEC’s website (http://www.sec.gov).  Copies of the proxy statement/prospectus and the filings with the SEC that will be incorporated by reference in the proxy statement/prospectus can also be obtained, without charge, by directing a request to the Needham’s Investor Relations via email at ir@needhambank.com or by telephone at (781) 474-5408, or to Provident Investor Relations via email at kfisher@bankprov.com or by telephone at (603) 318-2660.