After you rendezvous with Haurchefant, you go to inform Aymeric and Count Edmont of the latest events.
This quest is available if you have completed the quest Unrest in Ishgard.
Starting the Quest
Talk to Haurchefant in Ishgard to begin the quest.
Return to Fortemps Manor
Use an Aethernet Shard to go to the Last Vigil Aethernet Shard, then talk to the House Fortemps Guard to enter Fortemps Manor. 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 Lucia
Talk to Lucia to complete the quest.
Aether Current Quest
With the completion of this quest, you can now start the blue quest "Honoring the Past" in Ishgard. Completing that quest will attune you to an Aether Current in the Sea of Clouds.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: Ill-weather Friends. There will be a cutscene.