Old king left Queen's Master of Music (4,6)
I believe the answer is:
cole porter
'master of music' is the definition.
(Cole Porter was a musician)
'old king left queen's' is the wordplay.
'old king' becomes 'cole' (nursery rhyme character Old King Cole).
'left' becomes 'port' (left side of a ship - opposite of starboard).
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'cole'+'port'+'er'='COLE PORTER'
(Other definitions for cole porter that I've seen before include "US man of note" , "Man responsible for standards" , "Broadway composer" , "Let's Do It songwriter" .)