Agate is a quest item in The Witcher 3: Wild Hunt.
It can be found in Philippa Eilhart's quarters under Est Tayiar during Redania's Most Wanted. However, despite being a quest item, it doesn't serve a functional purpose other than Geralt commenting that Philippa wore several similiar agates around her neck, and it stays in the quest items inventory forever. It was part of cut content where Philippa was more heavily involved, but now only remains as a token item.