On this page of the Assassin's Creed Valhalla guide, you will find a detailed walkthrough for Edmund's Arrows side quest.
Rewards: 1,200 XP.
In the place marked in the picture above, you will find a long house. Go inside to meet a woman who admires a throne with many arrows stuck in it. The throne belonged to the recently deceased King Edmund.
Come up to the throne and collect at least one arrow (you must have free space in your inventory) and then talk to the woman in front of the throne.
Agree to sell the arrows to complete this task. The relic arrows are stored together with regular ones so you will have to sell them all. You can spend the money to buy new arrows in, e.g. Ravensthorpe.