Put out last, music programme on TV and radio at the same time? (9)
I believe the answer is:
simulcast
'programme on tv and radio at the same time?' is the definition.
'put out last music' is the wordplay.
'put out' indicates an anagram.
'last'+'music'='lastmusic'
'lastmusic' is an anagram of 'SIMULCAST'.
(Other definitions for simulcast that I've seen before include "entertainment" , "Same programme put out at the same time by two or more channels" .)