Small hospital behind mine (5)
I believe the answer is:
shaft
'mine' is the definition.
(thesaurus)
'small hospital behind' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'hospital' becomes 'h'.
'behind' becomes 'aft' ('aft' can be a synonym of 'behind').
's'+'h'+'aft'='SHAFT'
(Other definitions for shaft that I've seen before include "Long slender part or deep vertical opening" , "Ray (of sunlight)" , "Spear handle; ray of sun" , "Ray of light; spear" , "Handle - rod - passageway" .)