To begin your journey to Gorgon, you'll need to have completed the Radio Free Monarch quest. Once this quest has been completed, simply head back to the Unreliable and pick any destination, like Byzantium. Your travel will be interrupted by a special delivery!
Please note that save files that have reached the point of no return at the end of the game cannot be used to access the DLC, as it is not possible to leave Tartarus.
If you don't have any save files recorded before you entered Tartarus, then this may be a good chance to start a fresh new adventure and make completely different choices to see how they will affect the outcome of the game. It's worth mentioning that the Peril on Gorgon DLC also has multiple outcomes based on the choices that you make throughout your adventure on Gorgon, so be sure to keep that in mind!
If you meet the requirements to unlock the DLC, but for any reason are still unable to unlock the quest, take a look at this article to verify that the Peril on Gorgon DLC has been properly installed!