Duke abandoning minor conflict (3)
I believe the answer is:
war
'conflict' is the definition.
(war is a kind of conflict)
'duke abandoning minor' is the wordplay.
'duke' becomes 'd'.
'abandoning' suggests deleting specific letters.
'minor' becomes 'ward' (I've seen this in other clues).
'ward' with 'd' taken away is 'WAR'.
(Other definitions for war that I've seen before include "Combat" , "Major conflict" , "Hostile situation" , "Armed hostility" , "Open hostility" .)