Return to Gran Soren
Meet with Duke Edmun
Duel with the Duke
After defeating the dragon, head back to Gran Soren and meet up with the Duke. You'll have no choice but to fight him in a duel. Since you don't have any choice, engage him in battle and attack him until his HP is reduced to half. A cutscene will trigger afterward.
Escape the demesne. As you reach the Noble Quarter, you'll find Ser Maximillian waiting for you. Don't bother defeating the guards; just run to the Passage Gate and head to the Urban Quarter. Another cutscene will take place. The quest will be complete after the scene.