You need to apply for a new stormwater connection and include it in an existing building consent.
A building consent is needed because as-built private plans for the property need to be updated to reflect the changes.
If you don't have an existing building consent application, you will have to apply for one at the same time.
You will also need written permission from the property owner if the pipe runs through another property.
All connections must comply with the Building Act and the Stormwater Code of Practice.