I assume you live here and are not visiting? No worries as a non resident getting a FAL. Do what this site says to get your FAL. The entire possess takes one - two months (maybe longer if the AO is perticualry busy). costs $126.50. You need to be able to demonstrate that you can safely store firearms which means buying a gun safe. There are hunting jobs in NZ but you wont be getting one unless you find work with a pest control guy killing possums, are extremely good at head shooting animals out of a helicopter, or have years of experience in the NZ backcountry. If you have never hunted in NZ take the HUNTS course put on by the NZDA, It will give you a basic understanding of hunting in New Zealand.

If you are not living here, it is actually easier, do what this site says and apply for a Visitor's FAL.

I would recommend joining the NZDA if you have never hunted in NZ before, I don't know where you are from but the hunting is not like in the USA where they sit in stands and wait for deer to wander by, and joining a club with experienced kiwi hunters is a good start to gaining experience.

Finally the Department of Conservation is the go to for public land hunting. I find their field staff to be very helpful on animal locations, access etc. Obtaining a DOC permit to hunt mammals is very easy, visit thissite, give them your details including FAL number, tick the boxes of where you want to hunt, and that's it, 6 month hunting permit for free. Gamebirds and fish fall under different licenses. DOC maps is a useful tool for finding public land hunting areas, as well as tracks and huts.

Get stuck in anyways bro there is heaps of great hunting to be had in NZ.