Head of government's French bird almost mange par mauvais chat (9)
I believe the answer is:
taoiseach
'head of government's' is the definition.
(head of the Irish government)
'french bird almost mange par mauvais chat' is the wordplay.
'french bird' becomes 'oiseau' ('bird' in French).
'almost' means to remove the last letter (most of the word but not all of it).
'mange par' is an insertion indicator (\'eaten by\' in French).
'mauvais' indicates anagramming the letters (\'bad\' in French).
'oiseau' with its final letter taken off is 'oisea'.
'chat' anagrammed gives 'tach'.
'oisea' going into 'tach' is 'TAOISEACH'.
(Other definitions for taoiseach that I've seen before include "I 'ate chaos (anag) - Irish Republic's prime minister" , "Irish head of government" , "Irish PM" , "Irish premier" , "PM in Dublin" .)