Why doesn't my HBO show up on apple TV? I pay for the subscription through apple tv

if you have the HD or 4K model then did you go to app store and download the hbo app?

MacBook Pro 15″, macOS 11.0

On macOS, there are no external apps for streaming services, thus the TV app is not able to link to those apps on your Mac. This is different from iPhone, iPad, iPad Touch, or Apple TV box. See if you can use the web interface instead.