Troublemaker existed for revolution (5)
I believe the answer is:
devil
'troublemaker' is the definition.
(devil can informally mean a misbehaving child)
'existed for revolution' is the wordplay.
'existed' becomes 'lived' ('live' can be a synonym of 'exist').
'for revolution' shows that the letters should be reversed in order (letters revolve back).
'lived' backwards is 'DEVIL'.
(Other definitions for devil that I've seen before include "Demon" , "Beast" , "Fiend" , "Evil supernatural being" , "Beelzebub, Satan" .)