Odd claim about American entertainment (7)
I believe the answer is:
musical
'entertainment' is the definition.
(I've seen this before)
'odd claim about american' is the wordplay.
'odd' indicates anagramming the letters.
'about' indicates putting letters inside.
'american' becomes 'us' (abbreviation for United States).
'claim' with letters rearranged gives 'mical'.
'mical' placed around 'us' is 'MUSICAL'.
(Other definitions for musical that I've seen before include "Melodious" , "Drama where songs are more important than plot" , "Oklahoma, say" , "Annie maybe" , "Song and dance show" .)