I cannot find my Apple movie app on my tv

I pay $9.99 a month for my Apple TV app.

You may be paying for the Apple TV+ streaming service subscription. The app itself is free. The app itself does bring access to Apple TV+ and also a few other things.

It is not showing up on my tv.

On what make and model would that be?

The Apple TV app is supported on select not-too-old smart TVs (e.g. LG, Samsung, Vizio, Sony, Philips, HiSense, TCL, Panasonic), and on select TV-connected third party streaming devices (Roku, Fire TV, Xbox, PlayStation, Nvidia Shield, ‘Chromecast with Google TV’ dongle, select TV provider boxes that support apps), and select Apple devices (iPhone, iPad, iPod touch, Mac, Apple TV box).

If it is not pre-installed, then it may be downloadable from the on-device App Store (or however they name their app repository).

How to watch Apple TV+ and more - Apple Support

Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

Watch on these compatible smart TVs and streaming devices - Apple Support

The Apple TV App should be there on most Smart TV’s. The App has been redesigned and you can find your Apple tv + subscription in the App

• In the Apple TV App, swipe or click left to bring up the side menu and select Apple tv + .Or choose Store if you want to see movies to rent or buy. [Store content isn’t included in the subscription] Or choose Library - Purchase to see anything you’ve purchased or rented.

Use the sidebar to navigate the Apple TV app - Apple Support

The new design should be the same across all devices, if you’re accessing the App via a cable box app it might only be an Apple TV + App with an incomplete menu. It won’t have the Store.

The movie App is still available in the Apple TV box but has been redesigned to direct you to use the Apple tv App

• A smart tv might need a firmware update to refresh and update Apps.
• Also make sure you are signed into the App to view your subscription.

Or please describe which device you’re trying to use - it’s not entirely clear what you are asking.