Alphinaud asks you to join him to meet an Ishgardian dignitary who requested your presence personally.
This quest is available if you have completed the quest Back and Fourth.
Starting the Quest
Talk to Alphinaud in the Rising Stones in Revenant's Toll in Mor Dhona to begin the quest.
Speak with Minfilia
Enter the Solar and speak to Minfilia 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 Haurchefant
Go outside and go northeast to reach the Coerthas Central Highlands. Go northeast to where the orange arrow is pointing in the minimap. Enter the building and talk to Haurchefant. There will be a cutscene.
Speak with the House Fortemps Guard
Go outside and go around the corner of the building that you just came out of, to find the House Fortemps Guard. Talk to him and say Yes to proceed to the intercessory. 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 Alphinaud to accept the next quest: The Intercession of Saints.