If a governing body shall fail or decline to fill a vacancy in the membership of the governing body by appointment as provided in N.J.S. 40A:16-4 or 40A:16-5 within the time prescribed by N.J.S. 40A:16-12, the office shall remain vacant for the remainder of the term or until the election and qualification of a successor, as the case may be.
N.J.S. § 40A:16-13