The Google play store has it available for download. They give you a free trail when you subscribe and after the trial its like $50 a month.
would recommend you go through your signed in and trust device(s) normal way you would go to the you tube app and start the trial from there and not the separate app till you decide on continuing the service after the trial period. For a whole lot of reasons which don't happen often but when they do... boy are they ridiculous and just about impossible to correct. That's not a for this app type problem, it's in general for future endeavors too. I believe you can also try you tube music, premium, and the TV at one time. There is a selection to get the TV app right at the top of your you tube app settings menu.