Now that the wounded have been tended to, it is time to meet with the Crystal Exarch.
This quest is available if you have completed the quest Small Favors.
Starting the Quest
Talk to Thancred in the Crystarium to begin the quest.
Speak with the Crystal Exarch
Go southeast to where the orange arrow is pointing in the minimap. Talk to the Crystarium Gatekeep and say Yes to enter the Ocular. Talk to the Crystal Exarch to proceed. 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.
Speak with Minfilia
Go to the quest icon and talk to Minfilia to proceed.
Wait for Minfilia at Tesselation
Check on the Exit to the Crystarium and say Yes to exit the Ocular. Go to the Aethernet Shard and use it to go the Crystarium Aetheryte Plaza. Go west to where the orange arrow is pointing in the minimap and check on the sparkling Destination. There will be a cutscene.
Speak with Thancred
Go west to exit the Crystarium, then go southwest to where the orange arrow is pointing in the minimap. Talk to Thancred to proceed.
Speak with Hardyss
Go south to where the orange arrow is pointing in the minimap. Talk to Hardyss to proceed. There will be a cutscene.
Speak with Minfilia Again
Talk to Minfilia to complete the quest.