You need the relevant apps, TVNZ on Demand and the channel 3 app.

Load app, create account and then click "live tv". Pretty simple, only downside is you have to know which channel the content is on, there isn't a freeviewTV app for the apple that browses all networks (such a pity)

If you want a single app to do this (the same way as Kodi can do on other devices) then there are few choices.  These are the ones I have tried over the past few months:

MrMC - Kodi clone for Apple TV.  Free version, limited to 8 channels.  I cannot get TV1 and TV2 going but other channels play back fine.  Plays files from SMB fine
IPTVX - really nice interface and EPG.  Seems to play all channels.  Free version limits playback time.  I cannot get my downloads playing back or SMB.
LillyPlayer - free version works well, used this for a few months for streaming Freeview but could never get the EPG working

Otherwise, just use the individual apps as sen8or mentioned, but you are still limited compared to Kodi streams from Apsattv etc.

My personal view is that AppleTV is very limited in this area and I prefer to use Kodi on a Pi (or a Vero+, which is my next purchase for 4K support).

Thank you both for the advice. 

I may have to get a Vodafone TV then.