I see that "snapper" in the sense in which I use it in Post 3 doesn't appear in Chambers, though "snap" does. The snapper, in American football, is the center on the line of scrimmage who snaps the ball to the quarterback.
DOWN CLUE
Lineman in submissive role or important one? (14)
in submissive role: beneath whipper
important: in the sense pompous, self-important, pretentious
one: referring not to role but to person
hence important one/whippersnapper:
an insignificant but pretentious or cheeky person, often a young one