Box here perhaps showing my amusing broadcast (9)
I believe the answer is:
gymnasium
'box here perhaps' is the definition.
(boxers may train in a gymnasium)
'my amusing broadcast' is the wordplay.
'broadcast' is an anagram indicator (letters scattered or cast around).
'my'+'amusing'='myamusing'
'myamusing' anagrammed gives 'GYMNASIUM'.
'showing' is the link.
(Other definitions for gymnasium that I've seen before include "Athletics facility" , "Saying Mum (anag.)" , "Sports facility" , "room for horse jumping" , "School in Germany" .)