Hilarity left child with face flushed (8)
I believe the answer is:
laughter
'hilarity' is the definition.
(I've seen this before)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for laughter that I've seen before include "The expression of lively amusement" , "Manifestation of mirth" , "Chuckling" , "It's said to be the best medicine" , "Sign of amusement" .)