Duke and wise man backing artist (5)
I believe the answer is:
degas
'artist' is the definition.
(Edgar Degas, 1834-1917)
'duke and wise man backing' is the wordplay.
'duke' becomes 'd' (abbreviation).
'and' says to put letters next to each other.
'wise man' becomes 'sage' (sage is a kind of wise man).
'backing' is a reversal indicator.
'sage' in reverse letter order is 'egas'.
'd'+'egas'='DEGAS'
(Other definitions for degas that I've seen before include "Edgar ---, Fr. impressionist" , "Edgar -, French impressionist" , "Edgar -, Fr. artist" , "French artist known for his ballet scenes, d.1917" , "Edgar ---, ballet-dancer painter" .)