You split up to look for the terminal that may help you track down the archbishop.
This quest is available if you have completed the quest The First Flight of the Excelsior.
Starting the Quest
Talk to Cid in Azys Lla to begin the quest.
Search for an Active Terminal
Go to the sparkling Destination near Biggs and check on it. Then go south to the sparkling Destination near Alphinaud and check on it. Then go southeast to the quest icon on the map and check on the sparkling Destination near Estinien.
Speak with Cid
Go north to the quest icon on the map and talk to Cid.
Search for Wedge
Go southeast to where the orange arrow is pointing in the minimap. Go to the center of the orange circle to find a sparkling Destination. Check on it to proceed. There will be a cutscene.
Speak with Cid Again
Talk to Cid to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to the Guidance Node to accept the next quest: In Node We Trust.