If the power button on your Fire TV Stick remote isn’t working, you might need to enable a setting called HDMI CEC. This is a standard that allows two devices to communicate with each other via an HDMI cable. Provided your Fire TV remote has power and volume buttons, you should be able to use it to power off your TV.
While HDMI CEC is automatically enabled on your Fire TV Stick if the power button doesn’t work, follow these steps to manually enable the feature:
Open Settings on your Fire TV Stick.
Navigate to Display & Audio.
Select HDMI CEC Device Control to turn it on.
If this doesn’t fix the problem, you might also need to enable HDMI CEC on your TV. The location of this setting will differ based on your TV brand. Once done, press the power button on your Fire TV Stick remote. It should turn off your TV. If it doesn’t, try pairing the remote with your TV again by pressing and holding the home button for 10 seconds.