He came to trust Nick the same way he came to trust Carrie, through sheer pragmatism: Everything they ever said came true, all the way down the line. Nick may be a terrorist, and Carrie may be a nutcase, but that doesn't change the fact that their promises and guesses and secrets and admissions always worked out in the end.
What Carrie was to Brody, last year, is what Quinn has become to them. He has crawled into bed with them, and listened to them telling secrets. He is not impressed by love, but he knows what honesty looks like. And now, with this prayer, he knows another secret that not even Carrie gets to know. I wanted it to be a transcendent moment in which Nick's communion with God showed Quinn they were the same, but I don't know if it got that far. I just know that when we are alone, that is when we are unafraid. It's how Carrie fell in love, too.
David goes home after a long day of CIA things, a long day of waiting for the last loop to get closed on his war crimes, and is unpleasantly surprised at the uncommon visitor, the tiny man with the scrunched-up face, sitting in the corner of his bedroom. He does not jump for joy to discover Peter Quinn waiting in his bedroom because he is sick inside.
Quinn: "Here's the thing. Walden's dead, and Brody's leaving Congress. So there's no actual threat to the nation, there."
Estes: "Are you a CIA analyst? Because I'm pretty sure you're a dirty killer man."
Quinn: "You bet your ass I am. So listen up. Everything he ever said was true."
Estes: "That's exactly what I'm afraid of."
Quinn: "And then you have Carrie, who has ridden her bicycle all the way to saving the world. Two people that seem very compromised, but in fact are good folks."
Estes: "Your emotions make me want to vomit."
Quinn: "These are not emotions. They are true facts about the situation. Carrie is an asset to the CIA and to our country. Fact. Taking out Brody would be taking out two assets because she would fall apart like before, and never be reassembled. Fact. Which means that you are the only person who wants him dead, even though it works against your agency, which works against the country."
Estes: "Fine. I'll just have somebody else kill him, pussy."
Quinn: "No, you will leave him alone. Or I will murder you. Because you are a killer of little kids, and now you're covering your ass by getting rid of two people who just saved the world."