Simplified language broadcast for baby (6)
I believe the answer is:
pigeon
'for baby' is the definition.
(both can mean a concern or interest of someone)
'simplified language broadcast' is the wordplay.
'simplified language' becomes 'pidgin' (I've seen this before).
'broadcast' shows a homophone (sound like) (how the word might sound on the radio or TV).
'pidgin' is a homophone of 'PIGEON'.
(Other definitions for pigeon that I've seen before include "Short-legged bird" , "See 1 Across" , "Town and woodland bird" , "a visitor to Trafalgar Square" , "Homer, possibly" .)