Story from a Conservative to be important (7)
I believe the answer is:
account
'story' is the definition.
(synonyms)
'a conservative to be important' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'to be important' becomes 'count' (I've seen this in another clue).
'a'+'c'+'count'='ACCOUNT'
'from' acts as a link.
(Other definitions for account that I've seen before include "Bill - story" , "Story; bank service" , "Explanation of conduct" , "Report of an event" , "Bill - narrative" .)