Removal of quiet desire (5)
I believe the answer is:
purge
'removal' is the definition.
(I know that purge is a type of removal)
'quiet desire' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'desire' becomes 'urge' (I've seen this before).
'p'+'urge'='PURGE'
'of' acts as a link.
(Other definitions for purge that I've seen before include "Purify, clear out" , "elimination of opponents" , "Remove undesirable elements" , "Get rid of unwanted elements" , "pogrom" .)