Final month supported by a politician — leave quickly (6)
I believe the answer is:
decamp
'leave quickly' is the definition.
(I've seen this in another clue)
'final month supported by a politician' is the wordplay.
'final month' becomes 'Dec' (abbreviation for December).
'supported by' says to put letters next to each other (in a down clue, some letters hold up others).
'politician' becomes 'MP' (Member of Parliament).
'dec'+'a'+'mp'='DECAMP'
(Other definitions for decamp that I've seen before include "Abscond" , "Bolt" , "Run away (unseen)" , "Make off - from tent?" , "Split" .)