After you take steps to assist Ala Mhigo's recovery, Lyse has news to share with you.
This quest is available if you have completed the quest Return of the Bull.
Starting the Quest
Talk to Lyse in Rhalgr's Reach to begin the quest. There will be a cutscene.
Head to the Ruby Bazaar Offices
Teleport to Kugane and use the Aetheryte to go to the Ruby Bazaar. Go up the stairs and into the building. Talk to the East Aldenard Trading Company Aide and say Yes to enter the Ruby Bazaar offices. There will be a cutscene.
Speak with Alisaie
Go outside and use the Aethernet Shard to go to the Rakuza District. Go northwest to the quest icon on the map. Talk to Alisaie to complete the quest. There will be a cutscene. You will learn the emote Greeting.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: The Sword in the Stone.