N.J. Regulations, Possession of Nongame & Exotic Wildlife, Subchapter 4. Nongame and Exotic Wildlife, 7:25-4.2 Permit required:
“(a) Except as hereinafter provided, no person shall possess any nongame species or exotic species of any mammal, bird, reptile or amphibian unless such person has first received both the appropriate permit from the Department as listed in N.J.A.C. 7:25-4.6(a) as well as any other state, municipal, or Federal permits or licenses which may be required to possess such species. Any permit issued to an applicant by the Department for the possession of any animal shall not exempt that applicant from compliance with any other law of the State of New Jersey or any municipal or federal law… (b) No person shall liberate within this state any nongame species or exotic mammal, bird, reptile, or amphibian unless such person has first received a permit from the Department, which explicitly allows the release of nongame species or exotic mammals, birds, reptiles or amphibians.”
N.J. Regulations, Subchapter 21. Terrapin Regulations:
“Subchapter historical note. Subchapter 21, Terrapin Regulations, was adopted as R1981 d.198, effective July 9, 1981. See: 13 N.J.R. 405(a).
7:25-21.2 Designation of terrapin season
No person shall take, catch, possess, expose for sale or attempt to catch or take any Malaclemys palustris, commonly known as diamondback terrapin, except between November 1 and March 31.
7:25-21.2 Taking of terrapin
No person shall catch, take, or attempt to catch or take any terrapin from any of the waters of this state by means of a trap, pot, fyke, seine, weir or net of any description.
7:25-21.3 Size requirement
No person shall take, catch or possess any terrapin less than five inches long, measured lengthwise along the shell, not take or destroy eggs of any terrapin.”
So, you're supposed to have a permit before you take a terrapin, and you're not supposed to take any less than 5" long.
ETA: this information was easy to find when googling "new jersey diamondback terrapin laws"