If you are going to study in NZ for more than three months, you have to have a NZ student visa. (That is the same even though you have studied elsewhere before.) Here is the INZ web page
https://www.immigration.govt.nz/assi...ional-students about student visas in general. You will see there are links there to other pages with more detail. In particular, you will need the formal offer of a place. NZMA are very used to dealing with foreign students, so they will know what paperwork you have to have from them.