Leave secretly last month with a politician (6)
I believe the answer is:
decamp
'leave secretly' is the definition.
(I've seen this in another clue)
'last month with a politician' is the wordplay.
'last month' becomes 'dec' (short for December, last month of the year).
'with' says to put letters next to each other.
'politician' becomes 'MP' (Member of Parliament).
'dec'+'a'+'mp'='DECAMP'
(Other definitions for decamp that I've seen before include "Mizzle" , "Split" , "Move on" , "Run away (unseen)" , "Do a runner" .)