Check Apple menu -> System Settings -> Displays. Verify the display shows up there. If it doesn't, make sure that the HDMI input on the TV matches the number on the HDMI port of the TV, and try again. Use detect displays.
If it doesn't work, you may need to reboot the Mac.
If it still doesn't work, try adding the Display menubar icon from the System Settings and see if the display shows there. If it doesn't, it could be your adapter for HDMI needs more power. Many such adapters need the power of the notebook computer to be plugged into the adapter, and then the adapter in the notebook.
You may want to bring your Mac, and the adapter into an authorized service center where they can verify if the adapter is itself faulty or underpowered.