American composer is overlooking intro (4)
I believe the answer is:
ives
'american composer' is the definition.
(Charles Ives, 1874-1954)
'is overlooking intro' is the wordplay.
'is' becomes 'lives'.
'overlooking intro' means to remove the first letter (the letter which introduces the word is removed).
'lives' with its initial letter removed is 'IVES'.
(Other definitions for ives that I've seen before include "he composed" , "St -, Cornish resort" , "This classical composer" , "US composer, d. 1954 - US folk singer, d. 1995" , "American composer of Three Places in New England, d. 1954" .)