Worried US with cannier security (9)
I believe the answer is:
insurance
'security' is the definition.
(insurance is a kind of security)
'worried us with cannier' is the wordplay.
'worried' indicates an anagram.
'with' means one lot of letters go next to another.
'us' after 'cannier' is 'cannierus'.
'cannierus' is an anagram of 'INSURANCE'.
(Other definitions for insurance that I've seen before include "Cover against misfortune" , "Cover against loss" , "Indemnity" , "Such a policy guarantees" , "Safeguard" .)