In hospital department, torso cut into quarters (5)
I believe the answer is:
abode
'quarters' is the definition.
(both can mean where someone lives)
'in hospital department torso cut' is the wordplay.
'in' is an insertion indicator.
'hospital department' becomes 'ae' (A and E, Accident and Emergency department).
'torso' becomes 'body' (synonyms).
'cut' means to remove the last letter.
'body' with its last letter removed is 'bod'.
'ae' going around 'bod' is 'ABODE'.
'into' is the link.
(Other definitions for abode that I've seen before include "Home or domicile" , "House made of adobe" , "Place of residence" , "House, home" , "Pad" .)