Please specify the brand, model, and platform (smart OS), and if you can find it, the year of introduction for that model, as troubleshooting can be model-specific.
In general, try a cold restart for the TV. Either find a software Restart option for the TV in the menus, or temporarily disconnect from power. Next, check for TV system software updates, and install if available. Next, try deleting and re-installing the Apple TV app, if the TV allows for that.
When opening the fresh copy of the Apple TV app, first try signing in, through the side menu, then Settings, then Accounts. The app is intends to store the last used account, so that it opens with that the next time (unless you sign out, reset, or delete the app).
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support