Crossword Genius

Box here perhaps showing my amusing broadcast (9)

Ross

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" .)

I've seen this clue in The Times.
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