One has succeeded as an American composer (4)
I believe the answer is:
Here is my best explanation:
'an american composer' is the definition.
'one has succeeded' is the subsidiary indication.
'one has' becomes 'ive' (contraction of I have).
'succeeded' becomes 's' (genealogical abbreviation).
'as' is the link.
(Other definitions for ives that I've seen before include "This classical composer", "American composer of Three Places in New England, d. 1954", "COMPOSER", "Saint of Cornwall or Cambridgeshire", "Charles -, American composer (The Unanswered Question)", "US composer, Charles", "Composer of Three Places in New England, d. 1954", "he composed", "US composer, d. 1954 - US folk singer, d. 1995" and "St -, Cornish resort".)