An Irishman lives in Ireland and his nationality is Irish. An Australian lives in Australia and his nationality is Australian. Question: Somebody who lives in New Zealand is a New Zealander, but what is his nationality? It can't be New Zealander, can it????????
the adjective is New Zealand; he has New Zealand nationality. If filling in a visa form or something he could write New Zealand, or New Zealander, or maybe just NZ; I don't think authorities would mind