Conrad has some words for you before you proceed onward to The Peaks.
Requirements
This quest is available if you have completed the quest The Fortunes of War.
Starting the Quest
Talk to Conrad in The Fringes to begin the quest. There will be a cutscene.
Speak with the Ala Mhigan Resistance Gate Guard
Talk to the Resistance Guard and say Yes to cross the bridge.
Speak with Lyse
Go southeast along the bridge, then go east to where the orange arrow is pointing in the minimap. Talk to Lyse to proceed.
Speak with M'naago
Go northwest up the slope and follow the path as it curves clockwise, then when you see Alphinaud and Alisaie, go southeast and through the archway that the M Tribe Ranger is standing next to. Follow the path upward through the cave and attune to the Aetheryte that you find at the top. Then go to the quest icon on the map and talk to M'naago to complete the quest. 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.
Aether Current Quest
With the completion of this quest, you can now start the blue quest "Eyes Bigger than Her Stomach" at the Peering Stones in the Fringes. Completing that quest will attune you to an Aether Current in this area.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: The Lure of the Dream.