Dreadful secret involving quiet ghost (7)
I believe the answer is:
spectre
'ghost' is the definition.
('spectre' can be a synonym of 'ghost')
'dreadful secret involving quiet' is the wordplay.
'dreadful' is an anagram indicator.
'involving' indicates putting letters inside.
'quiet' becomes 'p' (music symbol for 'piano').
'secret' anagrammed gives 'sectre'.
'sectre' enclosing 'p' is 'SPECTRE'.
(Other definitions for spectre that I've seen before include "Ghost, phantom, apparition" , "Respect for a ghost" , "Enemy organisation for James Bond; ghost" , "Sceptre (anag.)" , "something seen as a threat" .)