Tour of Duty Main Story, Brotherhood of Steel Quest
This quest will be triggered or can be aquired when you complete Shadow of Steel quest.
Stages of "Tour of Duty" quest
1. Meet Knight-Captain Cade
In order to become an effective part of the Brotherhood, Elder Maxson has ordered me to tour the Prydwen and familiarize myself with her crew.
2. Meet Proctor Quinlan
He has an extra task for you.
2.1. (Miscellaneous) Collect Technical Documents for Proctor Quinlan
3. Meet Proctor Teagan
Trader - weapons, ammo, etc.
Come back to him after the tour is finished and you will get another quest - Feeding the Troops.
4. Meet Proctor Ingram
You can try to convince her to tell you the story of how she lost her legs.
5. Quest completed
I've completed my tour of the Prydwen, and introduced myself to some of the important members of her crew.
Next / new quests are Feeding the Troops (Brotherhood of Steel), Show No Mercy (Main Story, Brotherhood of Steel).