Alphinaud has ideas in mind for finding the trove that Arenvald spoke of.
This quest is available if you have completed the quest Arenvald's Adventure.
Starting the Quest
Talk to Alphinaud in Rhalgr's Reach to begin the quest.
Speak with Residents of the Ala Mhigan Quarter
Teleport to the Ala Mhigan Quarter in The Lochs and go to each of the orange circles on the map to talk to a Middle-aged Highlander, a Mature Maid, and a Retired Roegadyn.
Speak with Ernold
Go to the quest icon on the map and talk to Ernold.
Report to Arenvald
Go southwest to where the orange arrow is pointing in the minimap and talk to Arenvald to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: The Mad King's Trove.