Quiet private demonstrated (5)
I believe the answer is:
shown
'demonstrated' is the definition.
(thesaurus)
'quiet private' is the wordplay.
'quiet' becomes 'sh'.
'private' becomes 'own' (I've seen this before).
'sh'+'own'='SHOWN'
(Other definitions for shown that I've seen before include "Explained" , "Displayed" , "Demonstrated" , "Exhibited" .)