Duke, having lost weight, is a quite different duke (9)
I believe the answer is:
ellington
'duke' is the definition.
(I've seen this before)
'lost weight is a quite different duke' is the wordplay.
I cannot really understand how this works, but
'lost' could be 'l' (abbreviation in sporting league tables) and 'l' is present in the answer.
'weight' could be 'ton' (ton is a kind of weight) and 'ton' is located in the answer.
This explanation may well be incorrect...
'having' is the link.
(Other definitions for ellington that I've seen before include "One Duke" , "Duke (of jazz)" , "Duke - (Mood Indigo)" , "Musician" , "Duke --, twentieth century band leader" .)