How do I add HBO Max to my streaming options?

For what device is this?

Do you have an Apple TV box? If so, which model? Identify your Apple TV model - Apple Support

Apple TV (4th generation or later) offers an on-device App Store, where users can download apps from. Find apps in the Apple TV App Store - Apple Support. That is not available on earlier models.

Without Apple TV box, you will have to choose from the apps as offered by the TV/streaming device manufacturer. The Apple TV app alone doesn’t facilitate adding additional apps. The Apple TV app does offer select in-app Channels to subscribe to, but that doesn’t include HBO Max. [HBO tried that, then stopped when HBO Max launched, and completely discontinued a year later for existing channel subscribers.]

if it's an appletv hd (4g) or newer then you do so by going to the app store, if an older appletv model and its not available then you can't