Apple TV Continuous Play

Hi there, kendyl289.

I see that you'd like to be able to watch each episode in a season one right after the other using the Apple TV application, and I'm glad to help.

Watch movies, TV shows, and live content in the Apple TV app -- The TV app also includes an Up Next queue and the subsequent episodes should play after the previous show has finished. 

How to force an app to close on your iPhone, iPad, or iPod touch -- If it doesn't continue to the next episode automatically, force quit the TV app, if it's open, then restart your iPhone: Restart your iPhone -- Once it's back to the Home screen, see if subsequent episodes play as expected.

Let me know how that goes, and take care!

Does this option exist in the Apple TV Roku app? Because I'm having the same issue using apple tv on my roku and I've looked in settings and don't see that option anywhere.