If you are moving to a new house within the same calling region, yes you will be able to transfer your number to your new address, however if you are moving regions your number will change.
Why might I need a new phone number?
New Zealand is split in to calling regions that give you free calling locally within the area where you live. Outside of these areas, it is considered a toll call.
You can find a full list of the calling regions here on Wikipedia.
Want to keep calling friends and family without worrying?
Head to My Account and grab an unlimited NZ landline calling pack for $5 or 500 NZ mobile minutes for $15. That way, you never have to worry how much you’re calling and to where.