Quiet desire to clean up (5)
I believe the answer is:
purge
'clean up' is the definition.
(thesaurus)
'quiet desire' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano').
'desire' becomes 'urge' (I've seen this before).
'p'+'urge'='PURGE'
'to' acts as a link.
(Other definitions for purge that I've seen before include "pogrom" , "Cleanse or eradicate." , "Elimination of "undesirables"" , "elimination of opponents" , "Remove by cleansing" .)