With the horn to summon Hraesvelgr in hand, you prepare to depart from Moghome.
This quest is available if you have completed the quest Moglin's Judgement.
Starting the Quest
Talk to Moghan in Moghome in the Churning Mists to begin the quest.
Speak with Alphinaud
Go to the quest icon on the map and talk to Alphinaud.
Speak with Kan-E-Senna
Talk to Kan-E-Senna and 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 Moghan
Go west to the slope that leads to the western archway out of Moghome. Go up the slope and through the archway, then go to the quest icon on the map and talk to Moghan to complete the quest.
Aether Current Quest
With the completion of this quest, you can now start the blue quest "Road Kill" in the Churning Mists. Completing that quest will attune you to an Aether Current in this area.
Next Main Scenario Quest
After you complete the quest, talk to Moghan to accept the next quest: The Road to Zenith.