Contracted second hospital to manage most of Kent (8)
I believe the answer is:
shrunken
'contracted' is the definition.
(similar in meaning)
'second hospital to manage most of kent' is the wordplay.
'second' becomes 's' (common abbreviation).
'hospital' becomes 'h'.
'to manage' becomes 'run' (I've seen this before).
'most of' means to remove the last letter.
'kent' with its last letter taken away is 'ken'.
's'+'h'+'run'+'ken'='SHRUNKEN'
(Other definitions for shrunken that I've seen before include "Having become smaller" , "Shun kern to be made small" , "Reduced" , "Wizened" , "Shrivelled, withered" .)