In this quest, the game will just tell you to help the citizens of Far Harbor. However, it seems that you really need to do the not-so-optional quests to complete this quest.
(Optional) Help the Mariner
(Optional) Help Cassie Dalton
After completing the two optional quests, Teddy will approach you and tell you about the “Captain’s Dance”. After the conversation, this quest will be complete and the next quest, “Rite of Passage” will start.