After leaving hospital, pursue patient (4)
I believe the answer is:
case
'patient' is the definition.
(thesaurus)
'after leaving hospital pursue' is the wordplay.
'after leaving' is a deletion indicator.
'hospital' becomes 'h'.
'pursue' becomes 'chase' (chasing is a kind of pursuing).
'chase' with 'h' taken out is 'CASE'.
(Other definitions for case that I've seen before include "Wine buyer's quantity - dative, for example" , "Cover" , "Detective work" , "Item of luggage" , "Box or outer covering" .)