Use of the IPhone

What is your model Apple TV? Identify your Apple TV model - Apple Support

What did you buy 2 days ago? [iPhone | Apple TV box | HBO subscription]

What type of HBO subscription do you have? [ HBO Go | HBO Now | HBO Apple TV app Channel]

Note the that various types of HBO subscriptions are not exchangeable. HBO Go needs the HBO Go app; HBO Now needs the HBO Now app; HBO Apple TV app Channel needs the Apple TV app.

Subscribe to Apple TV channels in the Apple TV app - Apple Support

Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld

Assuming its a 4th gen or 4k Apple TV, download the HBO App from the App Store.

See here: Purchase and download apps on Apple TV - Apple Support