Six leaders from councils exert pressure on local deputy (4,9)
I believe the answer is:
vice president
'deputy' is the definition.
(I've seen this before)
'six leaders from councils exert pressure on local' is the wordplay.
'six' becomes 'VI' (Roman numerals).
'leaders from' says to take the initial letters.
'on' is a charade indicator (letters next to each other).
'local' becomes 'resident' (a resident of a particular area).
The first letters of 'councils exert pressure' is 'cep'.
'vi'+'cep'+'resident'='VICE-PRESIDENT'
(Other definitions for vice president that I've seen before include "Number two to 46, say" , "Second-in-command" , "VP" , "senior politician" , "Not in charge" .)