Ran back to argue, being biased (6)
I believe the answer is:
narrow
'being biased' is the definition.
(I've seen this in another clue)
'ran back to argue' is the wordplay.
'back' is a reversal indicator.
'to argue' becomes 'row' (to row with someone is to argue with them).
'ran' back-to-front is 'nar'.
'nar'+'row'='NARROW'
(Other definitions for narrow that I've seen before include "Constricted in width" , "Pinched" , "Sort of boat, escape, gauge or squeak" , "Conservative" , "Strict" .)