handgun licenced from new hampshire moving to arizona driving what need to do?

No license needed there. The Vollmer-McClure act provides that if traveling with firearms through areas where you might need a permit or that particular firearm is restricted or illegal you can do so if it’s unloaded, cased, and inaccessible. This only applies to while traveling, and can only do necessary stops in those areas (fuel, food, sleep, restroom, etc), it becomes null and void if you stop to visit your aunt in an unfriendly state.

You will pass through few if any areas where a handgun would need licensed. But just have it unloaded and packed away inaccessible and you’ll be fine. Obviously do not cut through Ontario along the way with a firearm. It might save a few miles, but the extra hassle of bringing a handgun into Canada legally will make the little extra driving to avoid it a wise move.