You will need to provide an import number to your agent if it's over a threshold.
You can apply for one via the customs website but usually the agent can apply on your behalf - takes about a day for customs to issue you with a number if the agent applies and 5 days if you apply directly.
Ups's nz agent will invoice you for the gst. You pay it and they ship it. They charge to store the item in their warehouse so do not delay.