Request to entertain royal composer (4)
I believe the answer is:
berg
'composer' is the definition.
(20th Century Austrian composer)
'request to entertain royal' is the wordplay.
'request' becomes 'beg' (begging is a kind of requesting**).
'to entertain' means one lot of letters goes inside another.
'royal' becomes 'r' (abbreviation).
'beg' going around 'r' is 'BERG'.
(Other definitions for berg that I've seen before include "South African hill - Austrian composer" , "famously cut short a transatlantic journey" , "trouble at sea" , "Austrian composer of 12-tone music, d. 1935" , "Mountain; shipping hazard" .)