Prize for one part of the hospital (5)
I believe the answer is:
award
'prize' is the definition.
(I know that prize can be written as award)
'one part of the hospital' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'part of the hospital' becomes 'ward' ('ward' is part of 'hospital').
'a'+'ward'='AWARD'
'for' is the link.
(Other definitions for award that I've seen before include "medal, perhaps" , "Grant, confer" , "Arbitrator's decision" , "Official prize in a draw" , "Give, grant" .)