This is one of two opposing side quests that involves the Thirsk Mead Hall , the other being The Chief of Thirsk Hall . As they cannot both be completed, this quest will be marked as failed if The Chief of Thirsk Hall is accepted.
Speaking to Bujold she will explain the situation. Choosing the first dialogue option will start the quest by volunteering to help eradicate the Rieklings. Helping the Rieklings prior to this quest will warrant the time spent with them voided.
Head to Thirsk Mead Hall
The quest will initiate and the objective is to kill eighteen Rieklings including the Chief . After retaking Thirsk Mead Hall , Bujold will ask the Dragonborn to become her second. Two options will be available; either have Bujold to go on ahead or to go with her. She will then ask the Dragonborn to go to Hrothmund's Barrow with her to acquire Hrothmund's Blessing .
Head towards Hrothmund's Barrow and Bujold will be there. She will ask the Dragonborn if they are ready and will go into the cave. (If she is not near the entrance of the barrow, wait for an hour until she arrives.)
Upon descending inside, they will come to a hall submerged in water. The water will subside as the Dragonborn walks forward and upon Bujold's approach. Upon entering Hrothmund's Barrow, there is a secret door to the right, before the water-filled chamber. There will be a chest at the end of the passage with some leveled loot and gems strewn about.
She will run towards the altar, indicating that she has found the axe. There will be two chests near the altar that can also be looted.
Bujold states that the Thirsk Mead Hall needs a new tradition and asks the Dragonborn to keep what happened to be a secret. The first option will result in a peaceful solution, the second will cause Bujold to become hostile. Ignoring either options will default to the first option.
Upon return to the hall, Thirsk Mead Hall will be restored to its original stature, opening the smithing area and new beds at the end of the hallway. When returning to Thirsk Mead Hall, Kuvar will approach asking of the situation at the Barrow.
If the player killed Bujold, they can choose to the tell the truth or lie. By telling the truth, he asks if that was the reason they killed Bujold. Kuvar will then informs them that he will keep the Hall open for the one who is worthy.
If the peaceful solution was chosen, they can tell Kuvar that Bujold was worthy (lie) or tell him the truth. By telling the truth, he is appalled that it is a bold and dangerous thing to accuse. Telling Kuvar the truth, he will turn to Bujold to confirm this accusation.
After the situation has been handled, new dialogue will open among all the members. And fetching quests will be available.
Note: Telling the truth in both situations will make Kuvar dislike the Dragonborn.