NZ's even worse than Australia with regard to excess of local, qualified, unemployed pilots.
Even if by some miracle you got a job offer, that wouldn't in any way qualify you for a work visa. The only people who can get into NZ by that route are "skilled migrants" whose skills are listed on the "Essential Skills Shortage List"
Essential Skills In Demand Lists . Pilot has never appeared on the list and I seriously doubt it ever will
The only other ways to a passport are either marrying a local, or qualifying as an "investor" if you have a spare $NZ10 million.
Sorry for being the bearer of bad news but if it makes you feel better you wouldn't have gotten a job there anyway, there are plenty of high time expat kiwis who'd love to go home but can't even get a job offer in the RHS of a small turboprop