Absurd claim about an American show (7)
I believe the answer is:
musical
'show' is the definition.
(I know that show can be written as musical)
'absurd claim about an american' is the wordplay.
'absurd' indicates anagramming the letters.
'about' means one lot of letters goes inside another.
'an american' becomes 'us' (abbreviation for United States).
'claim' is an anagram of 'mical'.
'mical' enclosing 'us' is 'MUSICAL'.
(Other definitions for musical that I've seen before include "Melodic" , "Show with singing and dancing" , "Show, with numbers" , "Eg, Cats or Evita" , "Drama where songs are more important than plot" .)