Business record of one Conservative aristocrat (7)
I believe the answer is:
account
'business record' is the definition.
(as in a business' books or accounts)
'one conservative aristocrat' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'conservative' becomes 'C' (UK political abbreviation).
'aristocrat' becomes 'count' (some European aristocracies have counts).
'a'+'c'+'count'='ACCOUNT'
'of' is the link.
(Other definitions for account that I've seen before include "Description; importance" , "Invoice - story" , "Reckoning; narrative" , "News report" , "books" .)