does apple tv hd support youtube tv? my old apple tv does not support youtube tv, just youtube.

I have not tried as it is only available in the USA.

Didn't find any YouTube TV app on my Apple TV 4K

It should work within USA:

Watch on TVs with streaming media players, smart TVs, and game consoles:

Download the YouTube TV app on select devices by searching “YouTube TV” in your device’s app store. Supported devices include select Amazon Fire TV devices, Roku players and TVs, Apple TV and Apple TV 4K, Vizio SmartCast TVs, Samsung & LG smart TVs, HiSense TVs, Xbox One, and more. Additional info.

Stream YouTube TV to your TV using Google Chromecast, TVs with Chromecast built-in like Android TV, AirPlay for Apple TV, or Google Smart Displays.

Yes, there is a Youtube app for the Apple TV HD and Apple TV 4K. You get it from the App Store on the device. Please ensure you have a strong network to support it.

Excuse me but what is YouTube TV?

Please use Google, in a couple of seconds I was able to find:

https://tv.youtube.com/welcome/?utm_source=pm&utm_medium=gs&utm_campaign=1006175