LEVENE: I got to get on the fucking board. (1.1.168)
It's always nice when a character just comes out and states their desire. This ambition—the ambition to get back on the board—motivates Levene throughout the play. It's what drives him, and it's what brings him down in the end.
MOSS: Now, he's got the leads, he goes into business for himself. (1.2.121-122)
You think when Moss looks in the mirror he sees a cowboy staring back at him? There's something about this guy that says he fancies himself a modern day gunslinger. His ambition is to be out there on his own, though he's not particularly willing to work for it or put his own neck on the line. In order to follow his ambition, he manipulates others.
MOSS: take the fuckin' leads out of the files… go to Jerry Graff. (1.2.218-219)
Once you get past Moss's desire to go work for himself, you get a glimpse at another ambition of his: revenge. Of all of the characters, he's the one who wants to do something to get back at the people he believes have ruled over him for too long.