Report back to the Chancellor | The Chancellor's Quarry Darksiders 2 Guide

Before leaving the [Soul Arbiter's Maze], find the stairs leading to the lower treasury (the above screen) for a chest with some random valuables. Go back to the arena and enter the room with the portal.

Exit the ruins, open the world map and travel to the [Eternal Throne]. Approach the Chancellor, initiate a conversation and select I have the Crown in the dialogue. This is when the quest comes to an end and you are rewarded with 1800 XP and 8000 gold for its completion.