Worthless singer on the radio (4)
I believe the answer is:
base
'worthless' is the definition.
(I've seen this in another clue)
'singer on the radio' is the wordplay.
'singer' becomes 'bass' (bass is a kind of singer).
'on the radio' indicates a 'sounds like' (homophone) clue.
'bass' sounds like 'BASE'.
(Other definitions for base that I've seen before include "Ignoble - HQ" , "unprincipled" , "Bottom support" , "Not worth much" , "Foundation; counterfeit" .)