Classical goddess quiet during the radio broadcast (9)
I believe the answer is:
aphrodite
'classical goddess' is the definition.
(Greek goddess)
'quiet during the radio broadcast' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'during' means one lot of letters goes inside another.
'broadcast' indicates anagramming the letters (letters scattered or cast around).
'the'+'radio'='theradio'
'theradio' is an anagram of 'ahrodite'.
'p' placed inside 'ahrodite' is 'APHRODITE'.
(Other definitions for aphrodite that I've seen before include "Atrophied (anag.)" , "Greek goddess of love, like Rome's Venus" , "Greek goddess equivalent to Roman Venus" , "Greek goddess of love, like Roman Venus" , "Sex goddess" .)