Can I get my order of protection from Arizona enforced in another state?
Yes. If you have a valid Arizona order of protection 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 orders of protection 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 order of protection is good under federal law? to find out if your order of protection qualifies.
Each state must enforce out-of-state orders of protection in the same way it enforces its own orders. Meaning, if the abuser violates your out-of-state order of protection, 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
1 18 U.S.C. § 2265; see also A.R.S. § 13-3602(R)