The Stolen Heirloom is a Shrine quest in The Legend of Zelda: Breath of the Wild. It is a quest given to Link by Impa at Kakariko Village. This quest allows Link to enter the Lakna Rokee Shrine after its completion.
There are tasks that need to be completed before the events of this Shrine quest can start, Link must have helped out Pikango in finding the Great Fairy Fountain and shown him a snapshot during the main quest "Find the Fairy Fountain". Link must have then found and wrangled up all ten of Cado's Cuccos during the side quest "Flown the Coop" and given Lasli five Sunset Fireflies during the side quest "By Firefly's Light".
Theft of the heirloom
Sometime later after Link has assisted these folks, Link goes to Impa's house to find her and Paya distraught over the missing Sheikah Heirloom. This orb used to sit on Impa's right-hand side because it had been stolen right from under them. It was stolen sometime during the darkest hour of the night, and Paya and Impa currently have no leads as to who might have done it as none of the Sheikah villagers would dare enter Impa's home so brazenly and snatch the Heirloom and believes that those who were not native to the village were innocent, too.
Later that night, starting at 22:00, Link would notice that Dorian, one of the gatekeepers of Impa, is walking away from his post and is talking to himself about something relating to the incident. Link keeps a low profile and stealthily follows Dorian to what appears to be a pedestal for an orb. Dorian stops, looking for someone, when he arrives there... While Link moves closer, a Yiga Blademaster reveals himself, and it turns out this is the culprit who had stolen the Heirloom. The Blademaster also reveals that Dorian had joined the Yiga Clan sometime in the past, and he had surrendered his life the moment he left them. The Blademaster is then poised to be rid of Dorian as his usefulness had come to an end, until he notices Link watching from nearby and decides to get rid of Link.
After the defeat of the Blademaster, Dorian then confesses to Link about everything that had taken place before he had become the gatekeeper. Dorian was formerly a Yiga clansman until he had met his wife. Because of this, Dorian had turned his back on the Yiga, married the woman, and had two children with her. All was well until his past had come back to haunt him: the Yiga had ambushed his wife and killed her and they threatened to do the same to Dorian's children, so Dorian was being blackmailed into being a spy for the Yiga Dorian told them everything: Link's presence, info about Kakariko, and likely more. When Dorian felt strong enough in that he was sure he could protect his young ones, he no longer feared them until they threatened the lives of Impa and Paya if he did not do what they said.
Dorian then explains that the Heirloom was the key to the Shrine and recommends that Link use it. When Link does, the Shrine of Lakna Rokee rises from the ground. After this, Dorian then asks Link to keep what had just transpired on this night a secret as he does not want his children, Koko and Cottla, to have to pay the price of his actions. From there on, Dorian pledges loyalty to Kakariko Village and leaves the scene.