N.Y. Pub. Off. Law § 43

§ 43. Filling other vacancies. If a vacancy shall occur, otherwise\nthan by expiration of term, with no provision of law for filling the\nsame, if the office be elective, the governor shall appoint a person to\nexecute the duties thereof until the vacancy shall be filled by an\nelection. But if the term of such officer shall expire with the calendar\nyear in which the appointment shall be made, or if the office be\nappointive, the appointee shall hold for the residue of the term.\n