Period in which radio nut broadcast (8)
I believe the answer is:
duration
'period' is the definition.
(I know that duration is a type of period)
'radio nut broadcast' is the wordplay.
'broadcast' indicates anagramming the letters (letters scattered or cast around).
'radio'+'nut'='radionut'
'radionut' anagrammed gives 'DURATION'.
'in which' acts as a link.
(Other definitions for duration that I've seen before include "Length of time" , "Around it (anag.)" , "Time scale" , "Period during which something continues" , "Term, span, time" .)