Haul part of hospital up (4)
I believe the answer is:
draw
'haul' is the definition.
(I know that haul can be written as draw)
'part of hospital up' is the wordplay.
'part of hospital' becomes 'ward' (hospitals have wards).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'ward' in reverse letter order is 'DRAW'.
(Other definitions for draw that I've seen before include "Tied score; sketch" , "2-2 in game, say" , "Even-scored game" , "Pull along; sketch" , "attractive thing" .)