Due to kill first fly (4)
I believe the answer is:
wing
'fly' is the definition.
(synonyms)
'due to kill first' is the wordplay.
'due' becomes 'owing' (similar in meaning).
'to kill first' means to remove the first letter (the first letter is killed off).
'owing' with its initial letter taken away is 'WING'.
(Other definitions for wing that I've seen before include "bit of a mansion" , "Faction; annexe" , "Group of squadrons; par of car" , "Arm adapted for flight" , "Take . . . . to fly like a bird" .)