N.J. Stat. Ann. § 26:3-7

If any vacancy shall occur on the local board of any municipality, other than a township which is subject to the provisions of subdivision C of this article, or a board established by a municipality that invokes the provisions of subsection b. of R.S.26:3-3, it shall be filled in the same manner in which the original appointment was made, but for the unexpired portion of the term only.