Permanent Residence does not expire (it is for life, and it's on record that you have it), but you can't use it to enter the country unless it is in a valid passport. INZ have recently started issuing eVisas even for residence (no sticker in the passport, and an official letter to carry with it and show if required), so you can notify them about your other passport and get one of those.
https://www.immigration.govt.nz/abou...-online/evisas If you would rather have a label, you have to request that separately and pay a fee for doing so.