A measure of the frequency injuries featured on the radio (5)
I believe the answer is:
hertz
'a measure of the frequency' is the definition.
(unit of frequency)
'injuries featured on the radio' is the wordplay.
'injuries' becomes 'hurts' ('hurt' can be a synonym of 'injury').
'featured on the radio' indicates a 'sounds like' (homophone) clue (as the word might sound on the radio).
'hurts' is a homophone of 'HERTZ'.
(Other definitions for hertz that I've seen before include "A measure of frequency" , "Cycles per second unit" , "Unit of frequency - German physicist, d. 1894" .)