If it works on your other TVs then the Firestick is OK, which means the problem is with that particular TV. Does the TV have more than one HDMI port? Have you tried the others?
At a guess, the TV may not be providing sufficient peripheral power on the HDMI port. https://www.quora.com/How-many-volts-does-an-HDMI-port-put-out
Answers & Comments
If it works on your other TVs then the Firestick is OK, which means the problem is with that particular TV. Does the TV have more than one HDMI port? Have you tried the others?
At a guess, the TV may not be providing sufficient peripheral power on the HDMI port. https://www.quora.com/How-many-volts-does-an-HDMI-port-put-out