To start the Peril on Gorgon quest line in The Outer Worlds, you will first need to complete the Radio Free Monarch quest on the planet Monarch. After that has been done, return to your ship and travel to another location in Halcyon. This will trigger Ada to inform you that another ship wants to dock with you. Accept the request and follow the dialog prompts to receive a parcel starting The Ones Who Walk Away from Gorgon main quest.