After what transpired at the Vault, you and Alphinaud go to the Congregation of Our Knights Most Heavenly to meet with Aymeric.
This quest is available if you have completed the quest A Knight's Calling.
Starting the Quest
Talk to Alphinaud in Isghard to begin the quest.
Speak with Aymeric
Use the Aethernet Shard to go to the Forgotten Knight Aethernet Shard and go east to the quest icon on the map. Talk to the Temple Knight Guard and say Yes to proceed. Talk to Aymeric to complete the quest. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Next Main Scenario Quest
After you complete the quest, talk to Lucia to accept the next quest: In Search of the Soleil.