Don't use any metal tools to clean the HDMI port, as you risk damaging it.

Insert the head of a brush, like a dry toothbrush, into the port, making sure the hairs surround the middle contact pad (the black tab in the middle of the HDMI port).

Gently turn the brush in small circles to break up any clumped debris.

Remove the brush and use a dust blower or compressed air to blow out any debris.

If any debris is stuck, reinsert the brush and rotate it to let the hairs "scoop" out any debris.

Plug in your device and check if it's working. If it's still not working, move on to the next step.