Matter resolved with hospital department: medical care (9)
I believe the answer is:
treatment
'medical care' is the definition.
(treatment is a kind of medical care)
'matter resolved with hospital department' is the wordplay.
'resolved' indicates anagramming the letters.
'with' says to put letters next to each other.
'hospital department' becomes 'ent'.
'matter' with letters rearranged gives 'treatm'.
'treatm'+'ent'='TREATMENT'
(Other definitions for treatment that I've seen before include "Discussion" , "patient progress" , "Medication" , "Management of something, illness say" , "Action to help" .)