Hey,
In most cases the requirement for an overseas license conversion to a ppl is usually a PPL standard BFR (bi-annual flight review). most training organizations should be able to help u with this... on top of that probably a NZ Air law exam as well. The best way could be to contact the NZ CAA a call in wellington and explain your situation and they should be of some help.....
In regard to training organizations..... it comes down to what type of aircraft u have currently been flying or wish to hire during your stay.... On top of that it depends were you are staying... I think that aircraft hire in parts of the south island require you to have mountain flying experience....
I hope i have been of some help....
If you have any other questions PM me...
NZ06AR