Emmanellain asks you to come with him to aid in his tasks in the Sea of Clouds.
This quest is available if you have completed the quest The Better Half.
Starting the Quest
Talk to Emmanellain in Fortemps Manor in Ishgard to begin the quest. There will be a cutscene.
Speak with the Airship Ticketer
Go outside and go north to the Hoplon, then go east down the curving stairway to reach the Tribunal Aethernet Shard. Attune to it, then go south down the curving stairway. Go east and attune to the Athenaeum Astrologicum aethernet shard, then go south to the orange circle in the map. The Airship Ticketer is near the center of the orange circle. Talk to the Airship Ticketer and say Yes to proceed. There will be a cutscene.
Speak with Emmanellain
Talk to Emmanellain to proceed.
Speak with Laniaitte
You will not be able to fly here yet. Go east down the stairs from the airship and go down to the aetheryte to the southeast. Attune to it, then go north to the wooden stairs and make your way down. Go southeast from there to where the orange arrow is pointing in the minimap, battling Gaelicats and Gastornises along the way. Talk to Laniaitte to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Laniaitte to accept the next quest: An Indispensable Ally.