Alphinaud has something to say, and asks you to meet him in the Intercessory at Camp Dragonhead.
This quest is available if you have completed the quest For Those We Can Yet Save.
Starting the Quest
Talk to Alphinaud in the Coerthas Central Highlands to begin the quest.
Wait for Alphinaud
Go to the Coerthas Central Highlands and go to the quest icon at Camp Dragonhead. Talk to the House Fortemps Guard between the wall and the southeast building and say Yes to proceed. Check on the sparkling Destination and there will be a cutscene. (Main Scenario 1 > Dragonsong Main Scenario Quests > Causes and Costs > Cutscene 1.)
Speak with Alphinaud
Talk to Alphinaud to proceed.
Speak with Alphinaud Again
Go outside and go west to the gate into Ishgard. Talk to the Temple Knight Gateguard and say Yes to enter Ishgard. Go northeast and use the Aethernet Shard to go to the Last Vigil Aethernet Shard. Go south to the quest icon on the map and talk to Alphinaud 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. (Main Scenario 1 > Dragonsong Main Scenario Quests > Causes and Costs > Cutscenes 2, 3, and 4.)
Next Main Scenario Quest
After you complete the quest, talk to the House Fortemps Knight to accept the next quest: The Man Within.