Go northeast to the massive building. Enter it and find yourself in the courtyard. There is a statue of Auriel here, but Serana points out that it's using the older signs of his power, so this temple must be ancient. Climb the stairs and pour water into the Basin. The water flows towards the star on the ground, and the Inner Sanctum door unlocks. Now that you have gained entry to the Inner Sanctum, you need to locate Arch-Curate Vyrthur.
Open the door and enter the Inner Sanctum. Go past a frozen Falmer, and towards the center of the Sanctum where some more frozen figures surround a shrine.
Climb up the platform and activate the Shrine of Auriel. This will cure all diseases and give you the Blessing of Auriel (other blessings will be removed). Open the door to the north, and through some corridors. Behind one of the room there is a frozen tunnel leading west and north. Take it, and eventually you get to the entrance to Auriel's Chapel.
Enter Auriel's Chapel. Vyrthur is located inside. He predicted you would come to him claming Auriel's Bow, and that you would bring your companion, Serana, to him with you. This appears to be some sort of a set up, or a trap.
All the Frozen Caurus and Frozen Falmers that are in the room come to life and attack you. Vyrthur also causes the ceiling to collapse on you. He also summons an Ancient Frost Atronach.
Eventually, once his minions are defeated, he creates a huge blast knocking you down, and then escapes to the balcony behind. Chase him with Serana. You catch up to him, and Serana demands he gives you the bow. Learn that Vyrthur is also a vampire, and is upset that Auriel did not prevent him from becoming one. Vyrthur created the prophecy, requiring Auriel's Bow and the blood of a pure vampire - the blood of a Daughter of Coldharbour.
After the conversation, Vyrthur becomes hostile. You need to slay Arch Curate Vyrthur. At this point Vyrthur is drained of powers and is pretty weak, so he shouldn't be that hard to kill.
Then, your objective is to speak to Gelebor, who appears below the balcony (you do NOT have to go all the way back to the Darkfall Cave). He tells you that the restoration of this wayshrine means that Vrythur must be dead and the Betrayed no longer have control over him. You tell him that the Betrayed weren't to blame. Vyrthur was a vampire, he controlled them, not the other way around.
You risked everything to get Auri-El's Bow, and in turn, you've restored the chantry. Knight-Paladin Gelebor can't think of a more deserving champion to carry it than you.