N.J. Stat. Ann. § 16:12-12

In the event of a vacancy in the office of warden or vestrymember caused by the failure of any candidate to receive a majority of the votes cast, the vacancy shall be filled at a special meeting of the parish, called forthwith and conducted as hereinafter provided. In the event of a vacancy caused by the death, resignation, removal, incapacity, refusal or neglect for six months of any duly elected warden or vestrymember to serve in such capacity, the vacancy may be filled by the vestry until the next annual meeting.