Cool political movement accepted by a doctor (6)
I believe the answer is:
aplomb
'cool' is the definition.
('aplomb' can be a synonym of 'cool')
'political movement accepted by a doctor' is the wordplay.
'political movement' becomes 'plo' (Palestinian Liberation Organization).
'accepted by' is an insertion indicator.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'a'+'mb'='amb'
'plo' put into 'amb' is 'APLOMB'.
(Other definitions for aplomb that I've seen before include "Cool self-assurance" , "Self-satisfied assurance" , "Cool self-confidence" , "Pompous dignity or poise" , "Self-satisfied dignity, complacency" .)