1
general::
Strive for, aim for, as in She's bucking for Editor of the Year. Strongly associated with seeking a promotion in the military, this expression originated in the late 1800s and is now applied more widely.
American Heritage Idioms
2
general::
Phrase(s): buck for something
Sl. to work ambitiously for something, such as a promotion. • I’m just bucking for recognition and, of course, a 20 percent raise. • You can tell by her attention to the boss that she’s bucking for promotion.
McGrawhill's American Idioms And Phrasal Verbs