Now that you are in Solstheim, you may have noticed that no quest has been triggered for you to start on the hunt for the Dragonborn. Apparently, you will be needing to do something in order for the quest to appear. Before you trigger the quest, have fun exploring Raven Rock first and get to know the people in Morrowind.
Once you are ready, simply head east from the entrance of the town.
How to Initiate the ‘Dragonborn’ questline
As you exit Raven Rock, you will encounter a High Elf commander being attacked by some creature. Help him defeat it to start a new questline. Once you are done, head to the north and find the three cultists that seem to be looking for someone.
One of the cultists will approach and tell you that you are the False Dragonborn! He will say something about Miraak and offers your heart to him. Be careful! They will attack you!
When they are all dead, find the leader of the cultists and loot his body. Within him will be a letter. Read it and you can then start your quest in finding the truth about the ‘Dragonborn’.