The arrow tells you to go left but the door is blocked. Instead go right (counterclockwise) and defeat the 4 princes to open 4 gates.
Defeat Prince Mkhai Karanahn to open the first gate. Defeat Prince Meti Karanahn to open the second gate. Defeat Prince Ati Karanahn to open the third gate. Defeat Prince Aka Karanahn to open the fourth gate.
Then defeat the final boss to complete the quest.