Naïve Democrat taken in by cool president (9)
I believe the answer is:
childlike
'naive' is the definition.
(similar in meaning)
'democrat taken in by cool president' is the wordplay.
'democrat' becomes 'd'.
'taken in by' means one lot of letters goes inside another.
'cool' becomes 'chill' (synonyms).
'president' becomes 'ike' (nickname of Dwight Eisenhower).
'd' placed inside 'chill' is 'childl'.
'childl'+'ike'='CHILDLIKE'
(Other definitions for childlike that I've seen before include "unsophisticated" , "Having the innocence of extreme youth" , "Innocent and trustful?" , "Showing youthful innocence" .)