Sorry, post is a bit confusing.
What happens when you try to access Apple TV outside of your computer?
How are you trying to access it?
Are you using the Apple TV app or Apple TV+ app on a Smart TV? If so, which make and model?
Are you using one of the apps on a streaming device? If so, which make and model?
Are you connecting your computer to a TV?
If using a smart TV or streaming device, have you logged in to your Apple account in it so it can access your subscription? Is the TV and/or streaming device connected to the internet in some way? Wi-Fi? Ethernet cable?
Not sure what the you think the antenna would do, since Apple TV is a streaming service, it uses an internet connection to work, it does not come over the air.
You'll need to explain exactly what you are doing to try to access Apple TV and what devices exactly are involved. here before any one can offer any advice.
start here ➜ Apple TV+ and Apple TV, How to watch on Smart TVs and streaming devices - Apple Support