How do I access my apple tv subscription on my smart tv.

Do you have the Apple TV app on a supported model smart TV?

List of Apple TV app-supported smart TVs and third party streaming devices - Apple

Then sign in to the Apple TV app, through the in-app Settings, with the Apple ID account that has the subscription.

All the ways to watch in the Apple TV app - Apple Support

Watch on your TV

Apple TV box (4K, HD, and 3rd generation) ﹥

Streaming devices ﹥

Smart TVs ﹥

Gaming consoles ﹥

Hmm, that is odd, that should work. Signing in with your Apple ID should cause the Apple TV app to recognize your Apple TV+ subscription, other Apple TV app Channel subscriptions, as well as any iTunes Store purchases and rentals linked to that account.

If the issue persists, contact Apple Support.