Authorising my MacBook Air to play downloaded movies on AppleTV

I have been downloading and watching movies on my MacBook Air for years. However, now I get a message saying my Mac is not authorised to play downloaded movies. I have tried clicking on my name in Apple TV so that I can authorise it (as instructed) but I do not get the option to select "Authorise". There is a message however saying only one device is authorised. What do I do?