Buscarron asks you to deliver a gift to the sylphs when you next meet with them.
This quest is available if you have completed the quest Into the Beast's Maw.
Starting the Quest
Talk to Buscarron in the South Shroud to begin the quest.
Deliver the Azeyma Rose Oil
If you haven't yet attuned to the Aetheryte east of here, you can go east from Buscarron's Druthers to reach aetheryte in Quarrymill, and after you attune to it, go northeast to return to the East Shroud. Then go northeast to Little Solace and talk to Knolexia to hand over the rose oil and complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Komuxio to accept the next quest: Believe in Your Sylph. There will be a cutscene.