Alphinaud requests leave to remain stationed in Ul'dah to lend the Braves' support to the Immortal Flames as they investigate the riots.
This quest is available if you have completed the quest Let Us Cling Together, and have completed the following series of quests, which must be done in order:
Starting the Quest
Talk to Minfilia in the Rising Stones in Revenant's Toll in Mor Dhona to begin the quest.
Speak with Riol
Exit the Solar and talk to Riol. There will be a cutscene.
Speak with Ilberd at Highbridge
Go to Eastern Thanalan and go to where the orange arrow is pointing in the minimap. Talk to Ilberd to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Ilberd to accept the next quest: Bait and Switch.