Follow the markers and talk to the named personnel in the ship. Head to the Power armor bay first and talk to Ingram. During the conversation, ask about your power armor and she’ll give you one.
Next, the nearest one from Ingram is Proctor Teagan, the ship’s quartermaster. He will also mention some extra work for you after you meet up with the other crew members.
Talk to Proctor Quinlan next and you’ll get the additional task of collecting technical documents for Proctor Quinlan. Finally meet the ship medic Cade who will ask you a series of questions. In his clinic, you can also get the Knight-Captain Cade holotape. After talking to all the four marked crew members, the quest will be complete and the next quest will become available immediately.