Igmund gives the Dragonborn a quest to recover Hrolfdir's Shield, the shield belonging to his father.
It cannot be completed if Thongvor Silver-Blood becomes Jarl of Markarth in Season Unending because Jarl Igmund will no longer offer the quest.
Due to the Radiant-Story Mechanic, the shield can be found in a variety of different locations depending on your level. Possible locations include: