After completing both The Lost Patrol and Show No Mercy, look for Captain Kells at the Prydwen's bridge for this assignment. This quest involves some missing supplies at Boston Airport, The Brotherhood's main ground base. You need to go down there and question the airport staff. Start with Knight-Sergeant Gavil.
Gavil has little patience for this issue, and while that might peg him as a likely suspect, he is at least helpful enough to suggest that you speak with Knight Lucia and Initiate Clarke. Question both of them on every available topic in the discussion trees. After exhausting all discussion topics, talk to Gavil again. With no concrete leads, he'll suggest you gather evidence aboard the Prydwen.
The waypoint indicator will point to Lucia and Clarke's storage lockers, and you'll find the evidence in Lucia's locker. Unlock it and play the holotape contained in the locker. Confront Lucia back at the airport with the evidence you found. She'll express concern about Clarke's well-being and request that you shadow him as he ends his shift.
If you discretely tail him, he'll lead you to the ruins below the airport, which is an abandoned subway system connecting the airport to the city. Explore the subway and the adjacent parking garage. Assuming you've explored every route possible, you'll eventually find yourself confronting Clarke and the reason for his sketchy behavior.
Depending on your charisma level, you can convince Clarke to lower his weapon. You could potentially spare him and keep his secret between you, but you will have to lie to Captain Kells. You can also spare him, then report his crime, and he will be sent to Cambridge Police Station. (You can free him during the Railroad's Precipice of War quest). Lastly, you can just kill him, which is easy to do, intentionally or not. Clarke doesn't like it when you kill Ghouls in front of him, and he will want to kill you if do so. Whatever you decide, report the outcome to Captain Kells to complete the quest.
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