Brief session Republican rejected (5)
I believe the answer is:
remit
'brief' is the definition.
(both can mean someone's responsibilities)
'session republican rejected' is the wordplay.
'session' becomes 'time' (a period of time).
'republican' becomes 'r' (abbreviation).
'rejected' shows that the letters should be reversed in order.
'time'+'r'='timer'
'timer' backwards is 'REMIT'.
(Other definitions for remit that I've seen before include "Pay; mail" , "Scope of prescribed job" , "Send < authorisation" , "Give up" , "Send back; scope of authority" .)