Succeeded in keeping hospital department (6)
I believe the answer is:
school
'department' is the definition.
'succeeded in keeping hospital' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'in' becomes 'cool' (I can't justify this - if you can you should believe this answer much more).
'keeping' is an insertion indicator.
'hospital' becomes 'h'.
'cool' enclosing 'h' is 'chool'.
's'+'chool'='SCHOOL'
(Other definitions for school that I've seen before include "Where 2 takes place" , "Train - group of porpoises" , "Instruct" , "building" , "Teach; group of fish" .)