How to pair AirPods Pro with a tv that is not Bluetooth compatible?

If the TV has an HDMI connection, then the Apple TV HD or Apple TV 4K set-top box would work here, for content originating from the Apple TV.

Otherwise, and as mentioned above, you’ll need some sort of headphones-to-Bluetooth adapter, if the TV has a headphone socket.

Check with the TV vendor support folks, and see if they have suggestions for whatever model TV you have here, too.

no, airpods only means of communication and audio is bluetooth

so unless your tv has an audio output port you can connect to a device that makes it into a bluetooth stream you can't

like this

2-in-1 Bluetooth Transmitter Receiver/Wireless 3.5mm Audio Adapter RX/TX (mytrendyphone.eu)

mind you even without this extra link bluetooth is not really known not to have a delay which makes it ok for music and even calls but notoriously poor for movies and games with audio and visuals not being in sync