I have a WiFi printer that does not support AirPrint. Currently, I use a linux system with CUPS to share that printer to my iOS devices. I'm thinking about replacing this linux box with an Apple TV for media playback, and it would be great to keep the print support too. I understand tvOS allows third-party apps to be written and installed using Xcode, so are there any existing apps that can do this?
Fbara is correct. You cannot print from an AppleTV. In looking at the current APIs that are inherited from the iOS platform I do not see anything that looks like it would be able to support printing. Apple does tend to lock these types of devices down. If you are interested in the types of apps that you could code and what APIs are available please see this Apple Developer article here.