Composer for King George the First, for example (5)
I believe the answer is:
grieg
'composer' is the definition.
(Norwegian composer Edvard Grieg 1843-1907)
'king george the first for example' is the wordplay.
'king george' becomes 'gr' (Georgius Rex).
'the first' becomes 'i' (I in Roman numerals eg Elizabeth I).
'for example' becomes 'e.g.' (short for 'exempli gratia', 'for example' in Latin).
'gr'+'i'+'eg'='GRIEG'
'for' is the link.
(Other definitions for grieg that I've seen before include "Edvard ---, composer" , "Composer of the incidental music for Ibsen's Peer Gynt" , "Norwegian composer (Peer Gynt)" , "Scandinavian composer, d. 1907" , "Composer of incidental music to Peer Gynt, d.1907" .)