After you defeat Baron von Quiveron, Leofric asks you to make a delivery to Horizon.
Requirements
This quest is only available if you started the game in Ul'dah, and you have completed the quest Heir Today, Gone Tomorrow.
Starting the Quest
Talk to Leofric northeast of Black Brush Station in Central Thanalan to start the quest.
Deliver the Antique Dagger
Go to Horizon in Western Thanalan and talk to Fufulupa to complete the quest.
Next Main Scenario Quest
After completing the quest, you will need to be at least level 13 to proceed to the next quest. After you reach level 13, talk to Fufulupa to accept the next quest: Following Footfalls.