A nobleman catching cold in story (7)
I believe the answer is:
account
'story' is the definition.
('account' can be a synonym of 'story')
'a nobleman catching cold' is the wordplay.
'nobleman' becomes 'count' (count is a kind of nobleman).
'catching' means one lot of letters goes inside another.
'cold' becomes 'c' (eg on taps).
'count' enclosing 'c' is 'ccount'.
'a'+'ccount'='ACCOUNT'
'in' is the link.
(Other definitions for account that I've seen before include "Financial statement" , "Financial record; narrative" , "Narrative or invoice" , "Statement of transactions and costs" , "judge" .)