Rebuild the old bridge that once joined Eldfell and Thule for Gurutz the oil merchant at Thule Abbey. When you're done meet him at his new house on Stone Village for the reward.
You can start this quest after the Break into Gurutz' house quest.
I would also advise not to start this quest until you have completed the Main Quest and have either the Maul of Healing or Maul of a New Age.
Talk to him and say that he looks unhappy.
He will say he's been thinking of a way to leave Thule and wants you to rebuild the bridge that used to join Eldfell and Thule.
You will receive the Rebuild the Old Bridge quest.
If you chose the good ending and have the Maul of Healing, go repair the bridge from the Thule Side.
If you chose the bad ending and have the Maul of a New Age, go repair the bridge from the Eldfell Side.
Go visit Gurutz in his new house in Stone Village. Its the top North House.
Say How's Business?
The Rebuild the old bridge quest will be solved and you'll receive 5000 gold.