Apple TV App not showing in App Store of Samsung TV US55NU8000

Neither the iTunes store nor the Apple TV+ service are available in Pakistan directly, and as such TVs sold there would not have the App available since there would nothing you could do with it. Samsung restricts app availability based on the region the TV is meant for.

https://support.apple.com/en-us/HT204411#europe

Some TVs may allow you to change the region they are set for, and may make apps available that where not available previously. May not work with all models.

https://ironsocket.com/setup/help/samsung-smart-tv-region-switch-guide

For Samsung, the Apple TV app will be among the default apps for compatible TV models with the up-to-date firmware.

* You do not even need to download it because it will appear in the Apps section on your TV.

* Note: If the Apple TV app does not appear in apps, then it is not compatible with your TV.

Do ask Samsung about the support for the app on your model TV. They are the ones that add it or not. It is apparently not an App Store item. Possibly regionality may be a factor? (In which country are you?)

The Apple TV app is also available on Apple TV box, Roku, and Amazon streaming devices, for any TV models that do not support the app natively.