New York Laws
Article 3 - Creation and Filling of Vacancies
43 - Filling Other Vacancies.

ยง 43. Filling other vacancies. If a vacancy shall occur, otherwise
than by expiration of term, with no provision of law for filling the
same, if the office be elective, the governor shall appoint a person to
execute the duties thereof until the vacancy shall be filled by an
election. But if the term of such officer shall expire with the calendar
year in which the appointment shall be made, or if the office be
appointive, the appointee shall hold for the residue of the term.