I want to get my UK passport renewed here in NZ. I have a re entry visa into Thailand which expires when my old passport expires. Will my re entry visa still be valid in my old passport when re entering Thailand before it expires?

Your re-entry permit (not a visa) will still be valid in your old passport.

Show both passports on entry to use it and immigration will stamp you into the country in the new passport.

After you enter the country you will need to go to your local immigration office to have your stamps transferred.