Bringing unopened, commercially packaged beef jerky produced by US companies into NZ has not been a problem. Simply declare it and keep it handy to show for inspection. We have done so on pretty much the last dozen trips we've made to NZ from the US. We've been thanked every time so far for declaring it and having it handy to show the NZ authorities -- then we've been allowed to bring it in to the country.
You'll win friends among the inspectors at AKL's baggage claim if you 1) DECLARE IT on your form and 2) tell the beagle handlers to bring their dog over to check out your bag with the beef jerky in it. The beagles score a hit and get praised with some "good boys" and attadogs. The handler typically will then take a quick look at the bag of jerky and make a note on your form that it's been inspected. This usually speeds thing up when you head through the inspection lanes.
Don't bother trying to bring beef jerky in to Australia though. The same commercially sealed package of beef jerky that you can declare and take into NZ will be seized by the Australian inspectors and burned.