how do I access my sportsnet subscription on my samsung tv through my apple tv app?

Are you sure you were using the Apple TV App on the previous TV. And not just the Apple TV physical box?

The Apple TV App and the Apple TV are 2 different things.

In the TV App scroll down to the Channels list and see if it appears there.

see: link-> Subscribe to Apple TV channels in the Apple TV app - Apple Support

If you are using the same Apple ID as before it should already be ac time there.

You can't.

The TV App does not support external App subscriptions. The 3rd party channels available in it require a special in app subscription.

Also there is no Sportsnet channel in the TV App.