To begin this quest you should speak with the captain of the Shark’s Tooth, Gelon, who can be found on the coast south of Pilgrim’s Landing. She has lost her ship and her crew with it, and wants you to investigate what might have happened to them. Begin your search by turning east and riding along the coast. Keeping to the grasslands on the coast will allow you to loot as much olive wood as possible in the landscape along the way. When you reach the bay south of the Hill of the Sacred War, you will be able to use Ikaros to identify the location of the shipwreck.
Swim out to it until you are directly above the wreck. From here you can take out the sharks by shooting at them from the surface of the water. When they are both dead, dive under to retrieve Gyke’s armband. Unfortunately, there is no trace of Gyke herself; the sharks seem to have made a meal out of her and the rest of the crew. You can now return to Gelon and inform her about the fate of her ship and lover. At the end of the dialogue you will have an opportunity to recruit her as part of the crew of the Adrestia.
Note: Be sure to open the ship menu of the Adrestia to place Gelon among your ‘special lieutenants’. She will provide a +10% boost to ship armour when equipped. You can replace ship lieutenants at any time, so you needn’t fear being stuck with one particular trait boost for a time.