Run one competitive event (4)
I believe the answer is:
race
'competitive event' is the definition.
(I know that race is a type of sports competition)
'run one' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'one' becomes 'ace' (ace has a value of one in some card games).
'r'+'ace'='RACE'
(Other definitions for race that I've seen before include "Stock" , "Contest; zoom" , "Care about contest" , "Running contest" , "See 23" .)