N.J. Stat. § 19:6-13: Vacancies; filling

A vacancy arising in a district board otherwise than by expiration of term shall be filled for the unexpired term in the same manner as the original appointment. The board shall certify the name and address of the person so appointed and the name of the district in which the vacancy exists to the clerk of the county and to the municipal clerk, and the person so appointed shall be notified in the manner above provided.