You could:
Draw a text frame, then click that pulldown and choose English (UK), and then from the menu use Edit > Defaults > Synchronize from Selection. That should then set the default for future text frames in that document.
If you then use Edit > Defaults > Save it might set them for future new documents, too.
Or, you could change the Language/Spelling setting in the Text Style named Base, if you are using text styles and using the default ones supplied by Publisher.
Or, you could install a copy of the English dictionaries for some other English variant, and call them en-NZ dictionaries. The FAQ will help you find dictionaries to download, and you could, for example, grab the US or UK dictionaries but install them as en-NZ rather than as en-US or en-UK. You would need to make a directory of that name and rename the files.
