Conservative supporter keeping millions coolly (6)
I believe the answer is:
calmly
'coolly' is the definition.
(cool can mean calm or collected)
'conservative supporter keeping millions' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'supporter' becomes 'ally' (I've seen this before).
'keeping' means one lot of letters goes inside another.
'millions' becomes 'm' (abbreviation).
'ally' placed around 'm' is 'almly'.
'c'+'almly'='CALMLY'
(Other definitions for calmly that I've seen before include "Quietly, placidly" , "With serenity" , "sedately, with self possession" , "Unflappably" , "In a peaceful manner" .)