N.Y. Pub. Off. Law § 39

§ 39. Filling vacancies in office of officer appointed by governor and\nsenate. A vacancy which shall occur during the session of the senate, in\nthe office of an officer appointed by the governor by and with the\nadvice and consent of the senate, shall be filled in the same manner as\nan original appointment. Such a vacancy occurring or existing while the\nsenate is not in session, including offices in which officers are\nholding over pursuant to the provisions of section five of this chapter\nor any other law, and offices vacant during the session of the senate,\nshall be filled by the governor for a term which shall expire upon the\nappointment and qualification of a successor but in any event such term\nshall expire at the end of twenty days from the commencement of the next\nmeeting of the senate.\n