Invoice a cold aristocrat (7)

I believe the answer is:

account

'invoice' is the definition.
(synonyms)

'a cold aristocrat' is the wordplay.
'cold' becomes 'c' (abbreviation, eg on taps).
'aristocrat' becomes 'count' (some European aristocracies have counts).
'a'+'c'+'count'='ACCOUNT'

(Other definitions for account that I've seen before include "Charge" , "Bill; description" , "Narrative or invoice" , "Financial statement" , "judge" .)

I've seen this clue in The Daily Express.

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