US anthem is broadcast, showing eagerness (10)
I believe the answer is:
enthusiasm
'eagerness' is the definition.
(I've seen this in another clue)
'us anthem is broadcast' is the wordplay.
'broadcast' is an anagram indicator (letters scattered or cast around).
'us'+'anthem'+'is'='usanthemis'
'usanthemis' with letters rearranged gives 'ENTHUSIASM'.
'showing' acts as a link.
(Other definitions for enthusiasm that I've seen before include "Ardour" , "Gusto; fervour" , "Zeal" , "Avidity" , "Intense and lively interest" .)