Having got bigger reaction to bad joke perhaps when broadcast (5)
I believe the answer is:
grown
'having got bigger' is the definition.
(grown means increased in size)
'reaction to bad joke perhaps when broadcast' is the wordplay.
'reaction to bad joke perhaps' becomes 'groan' (a bad joke might make you groan).
'when broadcast' indicates a 'sounds like' (homophone) clue (as it might sound on a radio broadcast).
'groan' sounds like 'GROWN'.
(Other definitions for grown that I've seen before include "Fully developed" , "Cultivated" , "Increased; raised" , "Mature; raised" , "Raised; having got bigger" .)