For Auckland.... (https://www.aucklandcouncil.govt.nz/building-and-consents/building-renovation-projects/heat-your-home/Pages/install-wall-insulation.aspx)
You will need to apply for a building consent if you're installing insulation in:
- an external wall
- an internal wall that is a fire separation wall.
You don't need a building consent or a resource consent for any other insulation projects.
Dosent mention replacing existing, so if replacing, Id say no paperwork required.