After you receive your earrings for the banquet, Momodi wants to see you off.

Requirements

This quest is only available if you started the game in Ul'dah, and you have completed the quest A Matter of Tradition.

Starting the Quest

Talk to Momodi in the Adventurers' Guild in Ul'dah to begin the quest.

Put on the Voice of the Just and Speak with Bartholomew

In the previous quest, you received the Voice of the Just (purple earrings). Equip them now. If they aren't in your Armory Chest, check your inventory. If you still can't find them, try typing /isearch Voice into the chat box to check where it might be. If you don't have them, talk to the Calamity Salvager east of the Miners' Guild and go to Purchase Quest Rewards > Purchase Quest Rewards to purchase another.

Then use an aetheryte to go to the Chamber of Rule, and go south to find Bartholomew. If the quest icon over his head is red, be sure to equip the Voice of the Just earrings. Then talk to Bartholomew. There will be a cutscene. Be sure to watch this one.

Speak with Rauban

Exit the inn room via the Heavy Oaken Door, then go to the Hall of the Flames, which is south of the Ul'dah Aetheryte Plaza. Talk to Raubahn to complete the quest.

Optional: Unlock a Dance Emote

Now that you have completed the quest, you can optionally unlock a dance emote here in Ul'dah. To do so, talk to P'molminn in the Ruby Road Exchange (southeast of the Ul'dah Aetheryte Plaza) to accept the quest "Help Me, Lord of the Dance".

Next Main Scenario Quest

After completing the quest, you will need to be at least level 15 to proceed to the next quest. After you reach level 15, talk to Raubahn to accept the next quest: The Ul'dahn Envoy.