In detail:

New Zealand has relatively loose drone laws, but you should still fly carefully and not endanger other people or animals. There are so-called “shielded operations”, where you can fly within no-fly zones (such as airfields). You have to look for a nearby object, e.g. a house, and then not fly higher than that house. Additionally you need a “barrier”, e.g. trees that would intercept the drone if it got out of control. You may not fly higher than the object and the barrier. The no-fly zones are shown on the official map. In parks or settlement areas other prohibitions may apply, which can be found on this website. For private and commercial drone pilots there are no differences, the same rules apply.

The New Zealand Aviation Authority has made an informative video on “Shielded operations”.

Exceptions:

If the drone weighs more than 25 kg, you can find out and register under part 102. In the vicinity of airfields you have to report directly to the responsible person. Night flights are permitted as part of a shielded operation.