A deterioration in police vessel (7)
I believe the answer is:
carotid
'vessel' is the definition.
(carotid is a type of blood vessel)
'a deterioration in police' is the wordplay.
'deterioration' becomes 'rot' (I've seen this in another clue).
'in' indicates putting letters inside.
'police' becomes 'CID' (abbreviation for Criminal Investigation Department).
'a'+'rot'='arot'
'arot' put inside 'cid' is 'CAROTID'.
(Other definitions for carotid that I've seen before include "Acid rot in major artery (7)" , "major arteries" , "Relating to neck arteries" , "Major artery in neck" .)