Staff regularly argue and run for supervisor (7)
I believe the answer is:
manager
'supervisor' is the definition.
(thesaurus)
'staff regularly argue and run' is the wordplay.
'staff' becomes 'man' (manning is a kind of staffing).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'and' says to put letters next to each other.
'run' becomes 'r' (cricket abbreviation).
The alternate letters of 'argue' are 'age'.
'man'+'age'+'r'='MANAGER'
'for' acts as a link.
(Other definitions for manager that I've seen before include "suit?" , "Executive or controller" , "Boss" , "Supervisor" , "Sports team runner" .)