Composer's heart dicky when rising (7)
I believe the answer is:
corelli
'composer's' is the definition.
(Arcangelo Corelli)
'heart dicky when rising' is the wordplay.
'heart' becomes 'core' (synonyms).
'dicky' becomes 'ill' (I've seen this before).
'when rising' says the letters should be written backwards.
'ill' reversed gives 'lli'.
'core'+'lli'='CORELLI'
(Other definitions for corelli that I've seen before include "Arcangelo, seventeenth to eighteenth century Italian composer, violinist" , "Marie - - , romantic 17" , "Captain -'s Mandolin (de Bernires)" , "A mandolin-playing Captain" , "Arcangelo --, Italian baroque composer" .)