Celebrity of American shows (4)
I believe the answer is:
fame
'celebrity' is the definition.
('fame' can be a synonym of 'celebrity')
'of american shows' is the wordplay.
'shows' says the answer is hidden in the clue.
'FAME' is hidden within 'of american'.
(Other definitions for fame that I've seen before include "Celebrity; stage musical" , "Favourable public reputation" , "Note" , "Repute" , "14 [BOWIE] recorded this" .)