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

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.

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 ﹥