Do I have to register my protection order in NJ in order to get it enforced?
No. According to federal law, which applies to all states, you do not have to register your protection order in order to get it enforced.1
NJ has guidelines in place that address registration of foreign (out-of-state) restraining orders. These guidelines give full protection to an out-of-state protection order as long as you can show the officer a copy of the order and can truthfully tell the officer that you believe the order is still in effect.2 The order does not have to be entered into the state or federal registry in order to be enforced by a New Jersey police officer, but the officer does need to believe that it is a valid (real) order.
1 18 U.S.C. § 2265(d)(2)
2 State of New Jersey Domestic Violence Procedures Manual, amended October 2008, section 7.3.3, available at https://www.judiciary.state.nj.us/family/dvprcman.pdf