On this page of the Assassin's Creed Valhalla guide, you'll find a detailed walkthrough of the Asgard side quest: Valhalla Bound.
Reward for completing the mission: 1200 XP.
In the place indicated on the image above, you will meet a warrior named Einherjar. When you speak with him, he will tell you about his last memory - how he died.
Once you convince him that it's not a dream and the Valkyries have indeed lifted his soul to Asgard, the warrior will loudly utter the oath and leave; the quest will be over.