Argument after work upset new religious leader (7)
I believe the answer is:
pontiff
'religious leader' is the definition.
(I've seen this before)
'argument after work upset new' is the wordplay.
'argument' becomes 'tiff' (I've seen this before).
'after' means one lot of letters go next to another.
'work upset new' becomes 'pon' (I am not sure about this - if you are sure you should believe this answer much more).
'tiff' after 'pon' is 'PONTIFF'.
(Other definitions for pontiff that I've seen before include "Bishop" , "High-priest" , "Religious leader" , "Head of the Roman Catholic church" , "Title for a pope" .)