Can I add another TV providers APP to Apple TV?

If you have a 2nd or 3rd gen ATV then you cannot add apps. If you have a 4th gen then you can search the App Store

As mentioned, on the Apple TV version 4. (The one with the black remote that has Siri), you can choose the content you want to download to it. (So long as they have an AppleTV app in the app store.)

Some of the more popular providers are listed here.

Contact Apple TV content providers - Apple Support

Some content requires you to get it "unlocked" by first going to a certain page of your AppleTV, which you then log into your current cable/fiber/satellite/IPTV provider and log in with the credentials they give you in order to verify that you subscribe to them in order to allow it to be unlocked on AppleTV too. Once unlocked it, AppleTV is supposed to remember this linkage you've made between the device and your subscription service.