Can I get my restraining order from New Jersey enforced in another state?
Yes. If you have a valid New Jersey restraining order that meets federal standards, it can be enforced in another state. The Violence Against Women Act, which is a federal law, states that all valid restraining orders granted in the United States receive “full faith and credit” in all state and tribal courts within the US, including US territories.1 See How do I know if my restraining order is good under federal law? to find out if your restraining order qualifies.
Each state must enforce out-of-state restraining orders in the same way it enforces its own orders, so if the abuser violates your out-of-state restraining order, s/he will be punished according to the laws of whatever state you are in when the order is violated - this is what is meant by “full faith and credit.”
1 18 U.S.C. § 2265(a)