Transfer a Skilled Migrant Category Resident Visa to a new passport

Has anyone had experience of transferring a Skilled Migrant Category Resident Visa to a new passport? I can’t seem to find the cost of doing that? As my passport is due in a few years, I’m debating on whether to renew it before applying for a visa and having it valid for another 10 years or potentially going through that process in NZ.

There’s a page on the inz website somewhere that tells you how to do it. I think it’s free if you get the electronic visa