Go away for a month with a politician (6)
I believe the answer is:
decamp
'go away' is the definition.
(decamping is a kind of going away)
'month with a politician' is the wordplay.
'month' becomes 'dec' (abbreviation for December).
'with' is a charade indicator (letters next to each other).
'politician' becomes 'MP' (Member of Parliament).
'dec'+'a'+'mp'='DECAMP'
'for a' is the link.
(Other definitions for decamp that I've seen before include "Fold tents and go" , "Make sudden breakaway" , "Split" , "Leave suddenly" , "Go away suddenly or secretly - leaving tent?" .)