Really a mystery writer, keeping quiet to run a TV show (4,5)
I believe the answer is:
soap opera
'tv show' is the definition.
(I've seen this before)
'really a mystery writer keeping quiet to run a' is the wordplay.
'really' becomes 'so' (both can mean 'extremely').
'mystery writer' becomes 'poe' (Edgar Allan Poe).
'keeping' means one lot of letters goes inside another (some letters kept inside).
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'to run' becomes 'r' (cricket abbreviation).
'poe' enclosing 'p' is 'pope'.
'so'+'a'+'pope'+'r'+'a'='SOAP-OPERA'
(Other definitions for soap opera that I've seen before include "Sentimental TV serial, sounds clean" , "TV drama series" , "Eg, Coronation Street" , ""Coronation Street", for example" , "TV show" .)