Successful in life? Not American fellow stranded on island (8)
I believe the answer is:
prospero
'fellow stranded on island' is the definition.
(character in Shakespeare's The Tempest)
'successful in life? not american' is the wordplay.
'successful in life?' becomes 'prosperous'.
'not' is a deletion indicator.
'american' becomes 'us' (abbreviation for United States).
'prosperous' with 'us' taken out is 'PROSPERO'.
(Other definitions for prospero that I've seen before include "The rightful Duke of Milan in The Tempest" , "Magician in the 5" , "magician on stage" , "Shakespearean role" , "Exiled king" .)