In your place, I would reply to the NZ teaching council and ask THEM to answer if you need to do the TP in NZ. Also, they are the people with years of experience of how people go about this, and they will probably know what visa you would need. (My GUESS from reading of various INZ information is that it will depend on how long you would need to be in the country. For instance, people can do a certain amount of study on a visitor's visa
https://www.immigration.govt.nz/new-...le-visiting-nz. or you might need a student visa - but the TC will have seen others going through this process.)