N.Y. Jud. Law § 180
When the official term of either surrogate of New York county will expire at the close of any year by the effluxion of time or the disability of age, the successor of each surrogate shall be chosen at the preceding general election. Vacancies otherwise occurring shall be filled for a full term at the next general election happening not less than three months after such vacancy occurs; and until any such vacancy shall be so filled, the governor, by and with the advice and consent of the senate if the senate shall be in session, may appoint and fill such vacancy, or if not in session the governor may appoint and fill such vacancy. Any such appointment shall continue until and including the last day of December next after the election at which the vacancy shall be filled.
N.Y. Jud. Law § 180