Verify that you are (still) signed in to the Apple TV app on your smart TV. Else the app wouldn’t know that you are subscribed already. On the Home Screen, navigate up to show the sidebar, which should have an option for Settings. In Settings, find the Account option, then sign in there, if that wasn’t signed in (with the correct account). Once signed in, the linked subscriptions should get unlocked, and you shouldn’t be asked to start a trial again.
If the Apple TV app misbehaves on your Samsung smart TV, then consider these troubleshooting steps from Samsung Support:
What to do if an app is not working on Samsung TV - Samsung Support
- Cold reboot the TV,
- Update the TV system software, if available,
- Delete and reinstall the misbehaving app (if deletion is supported for that app),
- Reset the ‘Smart Hub’ (like a factory reset for the apps part of the TV).
Settings﹥Support﹥Self Diagnosis﹥Reset Smart Hub﹥…
If you need further assistance after that, please contact Apple Support.