Bust-up possibly the result of this badly-behaved kid scratching bottom (3)
I believe the answer is:
bra
'bust-up possibly the result of this' is the definition.
'badly-behaved kid scratching bottom' is the wordplay.
'badly-behaved kid' becomes 'brat'.
'scratching bottom' means to remove the last letter.
'brat' with its last letter taken away is 'BRA'.
(Other definitions for bra that I've seen before include "one carrying chest" , "Underwear item" , "Female undergarment" , "I give a couple a lift" , "Chest supporter" .)