How can I renew my passport and transfer my LTR visa to a new passport while living in NZ?

Generally, when you get a new passport, you get a certificate from the embassy "this new passport X, is the replacement is old passport Y"

You take this passport to the immigration office (normally where your most recent entry stamp was, but I can't recall all details), and they basically "transfer" your entry stamp and your visa to the new passport.

Then it's all as if the new passport has it all. But you might be better off to bring the old one to immigration even doing stuff in case.

Ask the Thai Embassy in Wellington.

You want to enter Thailand with 6 months or more valid on your passport. Get your passport renewed before entering Thailand. You can check for the procedures on the website for American consulate near you or the US State Department. I renewed my passport with the US embassy in Bangkok. I had to mail my current passport and got my new passport mailed to me 3 weeks later. Carry both your old and new passports with you. When you enter Thailand go to the BOI office in Bangkok and they will get your LTR visa transferred to your new passport. Your new passport will have a new passport number.

Remember to update your passport information with Thai banks and your Thai phone number.

I don’t know what country you are from but there is probably a similar procedure for other countries.

Please check the LTR website, as it has information about most procedures. You can contact the LTR section for more details if you need.