N.Y. Pub. Hous. Law § 34
A vacancy occurring other than by reason of the expiration of the term of a member of an authority shall be filled for the unexpired term. The mayor of a city or village, or the town board of a town, may remove a member of the authority for inefficiency, neglect of duty, or misconduct in office, but only after the member shall have been given a copy of the charges against him and an opportunity to be heard in person or by counsel in his own defense at a public hearing. In the event of removal, the mayor of a city or village, or the town board of a town, shall file with the commissioner a record of the proceedings together with a copy of the charges made against the member and his or its findings thereon. Pending the determination of charges against a member, the mayor or the town board, as the case may be, may suspend him from office.
N.Y. Pub. Hous. Law § 34