Put with confidence in hospital department, deteriorate (7)
I believe the answer is:
entrust
'put with confidence in' is the definition.
'hospital department deteriorate' is the wordplay.
'hospital department' becomes 'ent'.
'deteriorate' becomes 'rust' (I've seen this before).
'ent'+'rust'='ENTRUST'
(Other definitions for entrust that I've seen before include "Charge (with) - put into the care (of)" , "Place in the care or protection of someone" , "Place in someone's care for test run" , "Confide" , "Give custody of" .)