Composer, singer who mostly improvised (8)
I believe the answer is:
gershwin
'composer' is the definition.
(George Gershwin, 1898-1937)
'singer who mostly improvised' is the wordplay.
'mostly' means to remove the last letter (most but not all of the word).
'improvised' indicates anagramming the letters (letters are improvised or randomised).
'singer'+'who'='singerwho'
'singerwho' with its last letter taken away is 'singerwh'.
'singerwh' with letters rearranged gives 'GERSHWIN'.
(Other definitions for gershwin that I've seen before include "George and Ira ..., American musical brothers" , "he noted" , "Ira -; US lyricist" , "Composer of Rhapsody in Blue, d.1937" , "SECOND PART OF 14" .)