Medal, say, for duke after a conflict (5)
I believe the answer is:
award
'medal say' is the definition.
(medal is a kind of award)
'duke after a conflict' is the wordplay.
'duke' becomes 'd' (abbreviation).
'after' says to put letters next to each other.
'conflict' becomes 'war' (war is a kind of conflict).
'a'+'war'='awar'
'd' put after 'awar' is 'AWARD'.
'for' is the link.
(Other definitions for award that I've seen before include "Grant - prize" , "Give, as an honour" , "Oscar, say" , "Grant made by a court of law" , "Grant, confer" .)