To begin your journey to Eridanos, you'll need to have unlocked access to the Stellar Bay landing pad. Once unlocked, talk to ADA who will invite you to watch the latest episode of Halcyon Helen's thrilling serial adventure.
If you currently have no save data recorded before entering Tartarus, upon attempting to load that save file, you'll be prompted with an option to create a new save file set before landing on Tartarus. Select "Yes", and you will be able to gain access to the DLC as well as complete any other ongoing quests that were not completed prior to your journey to Tartarus.
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 Murder on Eridanos DLC has been properly installed!