Sport is conflict with referee finally intervening (4)
I believe the answer is:
wear
'sport' is the definition.
(sport can mean to wear or display on one's person)
'with referee finally intervening' is the wordplay.
'with' means one lot of letters goes inside another.
'finally' indicates one should take the final letters.
'intervening' becomes 'war' (I can't justify this - if you can you should believe this answer much more).
The final letter of 'referee' is 'e'.
'e' inserted within 'war' is 'WEAR'.
'is conflict' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for wear that I've seen before include "Have on - deteriorate from constant use" , "Northern river - sport" , "Exhaust" , "Tackle" , "(Put on) clothing" .)