One has succeeded as an American composer (4)
I believe the answer is:
ives
'an american composer' is the definition.
(I've seen this before)
'one has succeeded as' is the wordplay.
'one has' becomes 'ive' (contraction of I have).
'succeeded as' becomes 's' (genealogical abbreviation. I am not sure about the 'as' bit.**).
'ive'+'s'='IVES'
(Other definitions for ives that I've seen before include "US composer, Charles" , "St -, Cornish resort" , "US composer, d. 1954 - US folk singer, d. 1995" , "Saint of Cornwall or Cambridgeshire" , "Charles -, American composer (The Unanswered Question)" .)