You've tried more than one cord in that jack to be sure it's the jack and not cord?
You've shined a bright light into the hole to see if there is any lint in there? Remove the lint and retry the port?
Any part of it work? Plug in a Mic and see if it can pick up sounds?
When you've plugged something into it, you've checked to be sure that it is the audio-out option selected in settings? Maybe it is not getting selected and you need to manually select it?
In other words, how confident are you that the port is dead? You might want to work through as much testing as you can to be sure before you want to seek out a repair.
If definitely dead, Apple or Apple service center will know much better than anyone here. But again, that's a port that is nearly bullet proof, refined towards perfection over decades. Odds of it being dead are not very high, so put it through the paces to confirm if you have not already.