A group of three turian officers can be found chatting inside Purgatory, in an alcove to the right of where James is located at the bar. Listen to their conversation to acquire the mission.
Alternatively, you can also acquire the mission if you choose to conduct Search and Rescue operations in Castellus. This second way of acquisition is possible even before the Purgatory becomes available on the Citadel. In this case, the journal entry for this mission is named Citadel: Banner of the First Regiment.
The Banner of the First Regiment is located on Digeris, the third planet in the Castellus system. Scan the planet to retrieve the item. Return to the Citadel and speak to the turian officer to finish the mission. If you retrieved the banner early, do note that access to Purgatory requires Priority: Palaven's completion.