Apple TV | Watching purchased movies in different regions

Can I watch movies I’ve purchased in the Apple TV store anywhere in the world?

Not “anywhere” in a literal sense, but NZ-to-CA might actually work for some (or many) titles.

The Apple Media Services terms and conditions [NZ] [CA] state that services are available to you in your ‘home country’ of that moment, meaning no guarantees for different countries, nor for switching countries.

When you change the country for your Apple ID account, then you get access to a different iTunes Store region, which will have a (partially) different movie catalog (with potentially different language support). Movie titles that are considered a matching Store item in both regions, may still be available to you after the switch. This might be the advantage in your situation, considering the cultural and language overlap.

An officially supported way to get all your movies over to the new country, is to download the movies on Mac (or PC). The downloaded copies get authorized as your purchases, even when not available in the new country, but you would have to stream locally (on the Mac or Home Sharing), as online streaming would try to access the new region’s iTunes Store instead of the downloaded copy.

Change your Apple ID country or region - Apple Support

I'd like to add some context and detail since the reply you were given assumes that you will change your AppleID account store to the new location (Canada). You have teh choice of changing your AppleID country location. If you choose to keep it as New Zealand, as long as you still have the ability to pay in New Zealand currency with a Kiwi bank account/credit card, you can keep your NZ Apple store purchases and watch them anywhere in the world.

We've kept our US-based Apple store purchases while living around the world, even after almost 15 years living outside of the US. Because I don't intend to permanently cut financial ties with the US, I retain a bank account from which I continue to pay for iTunes purchases in USD. As Urquhart1244 mentions, however, once you change the country location, you lose access to the purchases in the previous country.

Keep in mind, though, that you do NOT lose those purchases. They are still tied to your account but inaccessible until you change the location back, which includes a local payment method.

You’re welcome.