If you recently updated your laptop MacOS to Big Sur and you are trying to connect to your Apple TV, you may have discovered that the workflow has changed.
Here is where you can find Air Play on your updated laptop:
System Preferences -> Displays -> Display
Check the box in the lower left corner. Then click on the drop-down to find your Apple TV
OR (easier)
Click on the Control Center icon in the upper right corner. Select Screen Mirroring.
Now, select the Apple TV of your choice.
Click Here to learn more about Air Play with Big Sur