This children’s contest is in the bag (4,4)
I believe the answer is:
sack race
'this children's' is the definition.
The definition suggests a singular noun which matches the answer.
'contest is in the bag' is the wordplay.
I cannot really see how this works, but
'contest' could be 'race' (race is a kind of contest) and 'race' is found in the answer.
'bag' could be 'sack' (both can mean a container) and 'sack' is found within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for sack race that I've seen before include "Jumping contest" , "Novelty competition on school sports day" , "Get rid of nation" , "athletics contest" , "sports day event" .)