Pull up part of the hospital (4)
I believe the answer is:
ward
'part of the hospital' is the definition.
('ward' is part of 'hospital')
'pull up' is the wordplay.
'pull' becomes 'draw' (drawing is a kind of pulling).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'draw' back-to-front is 'WARD'.
(Other definitions for ward that I've seen before include "Councillor's area" , "One under the protection of another" , "Separate room" , "Hospital room; part of borough" , "Division of borough" .)