One promoting free movement Tory leader's demoted twice (4)
I believe the answer is:
lube
'one promoting free movement' is the definition.
(a lubricant makes movement easier or freer)
I don't understand the rest of the clue.
(Other definitions for lube that I've seen before include "Grease (abbr)" , "oil" .)
I've seen this clue in The Guardian.
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