Pressure on local leader (9)
I believe the answer is:
president
'leader' is the definition.
(type of leader)
'pressure on local' is the wordplay.
'pressure' becomes 'p' (abbreviation).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'local' becomes 'resident' (a resident of a particular area).
'p'+'resident'='PRESIDENT'
(Other definitions for president that I've seen before include "Celebrant" , "American leader" , "US leader" , "Lincoln, for example" , "Our head of state has a strange red instep" .)