Check out
www.caa.govt.nz , under a side button "pilots" there is a link to foreign license holders converting to NZ.
Nothing to hard, as long as you have a current license & medical they will grant you the basic equivilent license I believe. You may have to sit the flight test / or renewal procedure for any instructor ratings etc. but check out the site. All NZ organisations refer to it so they wont say anything different.
S2K