He died, supported by Duke in real push forward (7)
I believe the answer is:
obtrude
'push forward' is the definition.
(synonyms)
'he died supported by duke in real' is the wordplay.
'he died' becomes 'ob' ('ob.' can mean 'died' from the Latin obiit).
'supported by' is a charade indicator (letters next to each other) (letters go below - in down clue).
'duke' becomes 'd'.
'in' means one lot of letters goes inside another.
'real' becomes 'true' (similar in meaning).
'd' going into 'true' is 'trude'.
'ob'+'trude'='OBTRUDE'
(Other definitions for obtrude that I've seen before include "Become unwelcomely prominent" , "Stick out awkwardly" , "Make unpleasantly noticeable" , "Thrust oneself forward" , "Interfere" .)