Wealthy American's brother keeping silent in turn (5)
I believe the answer is:
oprah
'wealthy american's' is the definition.
(Oprah Winfrey)
'brother keeping silent in turn' is the wordplay.
'brother keeping silent' becomes 'harpo' (mute Marx brother Harpo Marx).
'in turn' says the letters should be written in reverse (letters turning around).
'harpo' in reverse letter order is 'OPRAH'.
(Other definitions for oprah that I've seen before include "- - Winfrey (TV)" , "Miss Winfrey" , "Chat show queen" , "American chat show host" .)