When I migrate, will I lose my current passport?

No, not necessarily. Firstly, you will enter as a permanent resident that does not affect your current status of citizenship. After 5 years you can apply for citizenship of New Zealand (but this is not mandatory). The New Zealand government to a universal dual-nationality (ie the holding of two passports), so you could retain your current passport and obtain a New Zealand passport as well your own country of citizenship allows dual-nationality, as this right must be reciprocal. If not, you will need to surrender your other passport in order to become a citizen of New Zealand.