Quietly set up goody-goody (4)
I believe the answer is:
prig
'goody-goody' is the definition.
(thesaurus)
'quietly set up' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'set up' becomes 'rig' ('rig' can be a synonym of 'set up').
'p'+'rig'='PRIG'
(Other definitions for prig that I've seen before include "humbug" , "Puritanical or arrogant and annoying person" , "Unpleasant arrogant person" , "Self-righteous moralist" , "Self-righteous hypocrite" .)