Island's broadcaster picked up (4)
I believe the answer is:
skye
'island's' is the definition.
(Scottish island)
'broadcaster picked up' is the wordplay.
'broadcaster' becomes 'sky' (Sky is a broadcast TV channel).
'picked up' indicates a 'sounds like' (homophone) clue.
'sky' is a homophone of 'SKYE'.
(Other definitions for skye that I've seen before include "Largest island of Scotland's Inner Hebrides" , "Large Scottish island" , "Scotland island" , "Scots isle" , "Portree's isle" .)