A grim, drunken politician on the move (9)
I believe the answer is:
migratory
'on the move' is the definition.
'a grim drunken politician' is the wordplay.
'drunken' indicates anagramming the letters.
'politician' becomes 'tory' (I've seen this before).
'a'+'grim'='agrim'
'agrim' with letters rearranged gives 'migra'.
'migra'+'tory'='MIGRATORY'
(Other definitions for migratory that I've seen before include "Of birds that move seasonally" , "Having lots of moves" .)