Little rascal destroying quiet, making racket (4)
I believe the answer is:
scam
'racket' is the definition.
(I've seen this before)
'little rascal destroying quiet' is the wordplay.
'little rascal' becomes 'scamp' (both can mean a mischievous person).
'destroying' suggests deleting specific letters.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'scamp' with 'p' taken away is 'SCAM'.
'making' acts as a link.
(Other definitions for scam that I've seen before include "Fraudulent action" , "Fraudulent trick or swindle" , "Swindle (Slang)" , "Rip-off" , "Swindle (sl.)" .)