Brief row over minute cuts (5)
I believe the answer is:
remit
'brief' is the definition.
(both can mean someone's responsibilities)
'row over minute cuts' is the wordplay.
'row' becomes 'tier' (a tier is a row of things).
'over' shows that the letters should be reversed in order.
'minute' becomes 'm' (abbreviation).
'cuts' is an insertion indicator (some letters cut their way into a word).
'tier' back-to-front is 'reit'.
'reit' going around 'm' is 'REMIT'.
(Other definitions for remit that I've seen before include "Area of responsibility" , "Transfer - area of authority" , "Dispatch" , "Put off" , "Send < authorisation" .)