Kill the three groups of mummies in the western part of the Priestess' Court. These are the ones on the upper level praying to the temple. Each group will drop an urn.
In the center of the platform is a raised square. The western side of the square (closest the wall) is a lighter colored triangular area. Place the urns in the triangle area, outside of the triangle does nothing. (Note: Only place a single urn in the triangle area. The game claims an urn and spawns a group. If there's another urn in the triangle, a few seconds later the current group will despawn and a new one will spawn in its place. The Priestess does not spawn in every group.)
Kill the Rin Priestess of the Fyr'Un and her two adds. They will often quickly despawn if not attacked immediately (but respawn on the mummies that drop the urns is roughly 5 minutes).
Make your way through the Statue Court along the aqueduct. When you get near the edge where it drops off into the pool, pause for a moment while the bridge rotates so that you may walk across it (don't forget to jump across the gap!).
Follow the aqueduct ahead and right until you reach the door to The Silent City. Click the door to complete the quest.