All three phrases show up on page 40 of Tinker Tailor Soldier Spy in a single sentence.
"He was waiting for a connect, working a letterbox maybe, or trailing his coat and looking for a pass from a mug like me."
The entire paragraph is:
Once more it was Smiley's turn to receive the heat of Tarr's charm: "So what's it all about, Mr. Smiley? See what I mean? It's little things I'm noticing," he confided, still to Smiley. "Just take the way he sat. Believe me, sir, if we'd been in that place ourselves we couldn't have sat better than Boris. He had the pick of the exits and the stairway; he had a fine view of the main entrance and the action; he was right handed and he was covered by a left-hand wall. Boris was a professional, Mr. Smiley; there was no doubt of it whatsoever. He was waiting for a connect, working a letterbox maybe, or trailing his coat and looking for a pass from a mug like me. Well, now listen: it's one thing to burn a small-time trade delegate. It's quite a different ball game to swing your legs at a Centre trained hood, right Mr. Guilliam?"
waiting for a connect - Merely waiting to meet somebody. A connect is a person's handler or contact.
The source is the novel itself. The term "connect" shows up in several places in the story. An example from the same book: "You want to know who his connect is out there - this magic guy in North Germany with a crock of gold that's going to make us millionaires overnight?"
working a letterbox - Watching a drop off point for an informant. A place where somebody places a "letter" for another to pick up.
The term, "letterbox" is used at multiple locations in the story (and other stories) as a term for where informants drop off materials for their handlers. For example, "Ever seen that bamboo scaffolding they use? Fantastic. Twenty stories high and the coolies swarm all over it with slabs of precast concrete. A bit of discard piping," he said, "handy at shoulder height. It seemed most likely if Irina was in a hurry, that the piping was the letterbox she would use."
The movie, Bridge of Spies, shows a letterbox in the scene where the Russian spy hides a fake nickel under the park bench. The park bench is the "letterbox", a place to put "mail" for pick up later.
trailing one's coat - An officer of one side acting as if he is a likely defector - drinking, complaining about his job, in the hope of attracting a recruitment offer from an enemy intelligence officer, with the object of recruiting the enemy as a double agent instead.
The source for "trailing one's coat" comes from the Wikipedia article on Tinker Tailor Soldier Spy.
looking for a pass - Hoping he can get a recruiter on the other side to defect and become a double agent. Think of how a man might make a pass at a woman in a bar hoping to flirt with her. He makes a pass, and if she reciprocates, the conversation continues to the next step.
Edit to add: John LeCarre claims he invented the spycraft jargon that shows up in his stories. This is mentioned in the Wikipedia entry on Tinker Tailor Soldier Spy.
