Quiet advocate for a flushing out of the old order? (5)
I believe the answer is:
purge
'a flushing out of the old order?' is the definition.
(eg a purge of political opponents)
'quiet advocate' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'advocate' becomes 'urge' (synonyms).
'p'+'urge'='PURGE'
'for' is the link.
(Other definitions for purge that I've seen before include "Eliminate or expiate" , "Purify, clear out" , "Get rid of unwanted elements" , "Cleanse, purify" , "Cleanse of unwanted elements" .)