N.J. Stat. § 19:6-19
If a vacancy arises in any county board from any cause other than expiration of the term, the secretary of the county board, within 5 days thereafter, shall in writing notify the Governor, the appropriate county committee chairman, county committee vice-chairlady, State chairman, State committeeman and State committeewoman of such vacancy, and within the same time notify the Governor in writing the date on which such notice was received by the county committee chairman. If the secretary fails to so notify, any member of the county board may make such notifications. Within 10 days after receipt of notice by such county committee chairman, the county committee chairman, county committee vice-chairlady, State chairman, State committeeman and State committeewoman shall jointly nominate a successor, and any such nomination shall be made and certified in the same manner as provided in section 19:6-18 of the Revised Statutes, and the person so nominated shall thereupon be commissioned by the Governor. All appointments to fill vacancies shall be for the unexpired term only.
N.J.S. § 19:6-19