Converting you NZ licence to a UK ATPL is a massive undertaking. I know, I did it...
You will need to become a NZ resident to fly for a NZ airline. That may not be such a massive undertaking, however you will then pit yourself against hundreds of NZers looking for a handful of jobs. I know, I came to the UK to avoid this!
Getting into Air NZ or any of the Link companies is also a major accomplishment - many fall by the wayside.
The grass is not always greener. NZ is a fantastic place, however the UK job market is a lot bigger...