Area of responsibility, issue king must get on top of (5)
I believe the answer is:
remit
'area of responsibility' is the definition.
(remit can mean one's responsibilities or duties)
'issue king must get on top of' is the wordplay.
'issue' becomes 'emit' (both can mean to give out or radiate).
'king' becomes 'R' (abbreviation for rex, king in Latin).
'must get on top of' says to put letters next to each other (some letters go on top of others).
'emit' put after 'r' is 'REMIT'.
(Other definitions for remit that I've seen before include "Send; abate; cancel" , "Send < authorisation" , "Pay; mail" , "Orders" , "Timer (anag.)" .)