Count Edmont wishes to speak to you about your time with Lord Artoirel and Lord Emmanellain.
This quest is available if you have completed the following quests:
Starting the Quest
Talk to the House Fortemps Steward in Fortemps Manor in Ishgard to begin the quest. There will be a cutscene.
Speak with Edmont
Speak with Edmont in Fortemps Manor to proceed.
Speak with Aymeric
Go outside and use the Aethernet Shard to go to the Forgotten Knight Aethernet Shard. From there, go east and go through the door behind Firmalbert. Go to the quest icon in the map and talk to Aymeric. 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 west to go outside, and use the Aethernet Shard to go to the Tribunal Aethernet Shard, or, if you have not attuned to it, go to the Last Vigil Aethernet Shard and go north, then go east down the curving stairway to reach The Tribunal. Attune to the Aethernet Shard.
From the Tribunal Aethernet Shard, go northeast to enter the Tribunal and find Haurchefant. There will be a glow around him, indicating an instanced battle. Check on him and there will be a cutscene, and then the battle will ensue.
Solo Duty: Divine Intervention
Focus your attacks on Ser Paulecrain Coldfire until an Ishgardian Steel Chain appears around Alphinaud. Attack the Ishgardian Steel Chain until it is destroyed, then resume attacking Ser Paulecrain. Destroy any more Ishgardian Steel Chains whenever they appear.
If lighting orbs appear around the area, go outside of the metal square in the floor, some place away from Alphinaud, and if glowing lines appear beneath you, step off of them to avoid damage.
When Ser Paulecrain is defeated, focus your attacks on Ser Grinnaux the Bull, destroying Ishgardian Steel Chains if they appear, until Grinnaux is defeated.
After the battle, there will be a cutscene.
Speak with Haurchefant Again
Talk to Haurchefant to complete the quest. There will be a cutscene. You will receive a Black Chocobo Whistle from Haurchefant. Be sure to use it to obtain the Black Chocobo Mount.
A Note About Flying
You will now have access to the Aether Compass in Main Menu > Duty > Collection. You can drag it to a hotbar or add it to a crossbar. You can use it in Heavensward areas (e.g. the Coerthas Western Highlands and the Sea of Clouds) to see the bearing and distance to the nearest Aether Current. When you find an Aether Current, check on it to attune to it. Note that some Aether Currents will be unreachable until you have progressed farther in the story.
You can see your progress in Main Menu > Travel > Aether Currents. Note that you will also need to undertake certain blue quests to unlock additional Aether Currents for each area. These blue quests will be mentioned as they become available.
Next Main Scenario Quest
After you complete the quest, talk to Haurchefant to accept the next quest: Disclosure.