Gold diamond necklace is a quest item in The Witcher 3: Wild Hunt. During the secondary quest The Price of Honor, after finding the letter and key on one of Timmon's brothers' bodies, you can go back to where Agda's body was found and see a ship's mast out in the water. There's a sunken chest there with this inside.
You can choose to return this or not if it was retrieved before turning in the quest.
- The necklace, if Geralt keeps it for himself, can be sold or dismantled; the latter option, however, only yields iron ore.