N.J. Stat. § 40:41A-35
The office of county executive shall be deemed vacant if the incumbent moves his residence from the county or he is by death, physical or mental illness or other casualty unable to continue to serve as county executive. Any vacancy in the office of county executive shall be filled by election for the unexpired term only at the next general election occurring not less than 51 days after the occurrence of the vacancy, except that no such vacancy shall be filled at the general election which immediately precedes the expiration of the term in which the vacancy occurs.
In the event a vacancy eligible to be filled by election hereunder occurs on or before the sixth day preceding the last day for filing petitions for nomination for the primary election, such petitions may be prepared and filed for nomination in that primary election in the manner provided by article 3 of chapter 23 of Title 19 of the Revised Statutes.
In the event the vacancy occurs after that sixth day preceding the last day for filing petitions for nomination for the primary election, a political party may select a candidate for the office in question in the manner prescribed in subsections a. and b. of R.S. 19:13-20 for selecting candidates to fill vacancies among candidates nominated at primary elections. A statement of such selection under R.S. 19:13-20 shall be filed with the county clerk not later than the 48th day preceding the date of the general election.
Besides the selection of candidates by each political party, candidates may also be nominated by petition in a manner similar to direct nomination by petition for the general election; but if the candidate of any party to fill the vacancy will be chosen at a primary election, such petition shall be filed with the county clerk at least 55 days prior to the primary election; and if no candidate of any party will be chosen at a primary election, such petition shall be filed with the county clerk not later than 12 o'clock noon of the day on which the first selection meeting by any party is held under this section to select a nominee to fill the vacancy.
When the vacancy occurs, the county clerk of the county shall forthwith give notice thereof to the chairman of the county committee of each political party.
During the temporary absence or temporary disability of the county executive the chief administrator shall serve as acting county executive.
N.J.S. § 40:41A-35