Cowboy's contest (5)
I believe the answer is:
rodeo
'cowboy's contest' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for rodeo that I've seen before include "Mounted exhibition" , "Cowboy competition, riding horses and bulls" , "Horse sporting event for cowboys" , "Originally, a round up of cattle" , "Contest of cowboy skills" .)