Installing Apps on 4th and 5th Gen Apple TV: Yes
If you have the 4th generation Apple TV, which Apple introduced in Sept. 2015, or the Apple TV 4K, aka the 5th generation model, that debuted in Sept. 2017, you can download Apple TV apps to it. Those versions of the Apple TV are built around the idea that, as Tim Cook said when introducing the 4th gen. model, apps are the future of television. Installing apps on the 4th or 5th gen. Apple TV is similar to and just as easy as, installing them on an iPhone or iPad. The operating system that runs on the Apple TV, called tvOS, is slightly different from iOS, so the steps for installing apps on it are slightly different, too. Just like on the iPhone and iPad, you can redownload apps on Apple TV, too. Go to the App Store app on your Apple TV, select the Purchased menu, and then select Not on This Apple TV for a list of apps available for redownload.
Installing Apps on 1st, 2nd, and 3rd Gen Apple TV: No
Unlike with the newer models, users cannot add their own apps to the 3rd, 2nd, or 1st generation Apple TV models (except in one case, as we’ll see). That’s because the 3rd generation Apple TV and earlier models don’t have an App Store for third-party apps. But that doesn’t mean that new apps don’t get added. While users can’t add Apple TV on their own to these Apple TV models, Apple adds them from time to time. When the Apple TV debuted, it had less than a dozen channels of Internet content. By the time Apple stopped making these models, there were dozens. There was generally no warning when new channels appeared, and users couldn’t control if they were installed or not. When you turned your Apple TV on, you’d find that a new icon had appeared on the home screen and that you now had new content available. For example, the WWE Network wrestling streaming service simply appeared on Apple TV screens with no advance warning when it launched in Feb. 2014. Sometimes Apple bundled new apps in with updates to the Apple TV’s software, but new channels often debuted as they were ready.