We do ship to NZ.
Please note for shipments over NZ$ 400, you will be charged import GST and applicable duties at the NZ border.
More details here:
NZ Post should contact you, however if you don't receive any notifications, put your tracking number into the NZ Post website: https://www.nzpost.co.nz/
It has instructions for clearing customs. You'll also need to email them your invoice.