Depressed duke thrown out (8)
I believe the answer is:
dejected
'depressed' is the definition.
('deject' can be a synonym of 'depress')
'duke thrown out' is the wordplay.
'duke' becomes 'd' (abbreviation).
'thrown out' becomes 'ejected' ('eject' can be a synonym of 'throw out').
'd'+'ejected'='DEJECTED'
(Other definitions for dejected that I've seen before include "Downcast" , "Depressed and cast down" , "Down in the mouth" , "Melancholy" , "Downhearted" .)