Dismiss people from competition (4,4)
I believe the answer is:
sack race
'competition' is the definition.
(I know that sack race is a type of race)
'dismiss people' is the wordplay.
'dismiss' becomes 'sack' (synonyms).
'people' becomes 'race' (people can mean a national group or race).
'sack'+'race'='SACK-RACE'
'from' is the link.
(Other definitions for sack race that I've seen before include "jumping event" , "Novelty competition on school sports day" , "sports day event" , "athletics contest" , "event - with 10d" .)