Out of hospital, listen to chest (3)
I believe the answer is:
ark
'chest' is the definition.
(historical term for a chest)
'out of hospital listen' is the wordplay.
'out of' is a deletion indicator.
'hospital' becomes 'h'.
'listen' becomes 'hark' (harking is a kind of listening).
'hark' with 'h' taken out is 'ARK'.
'to' is the link.
(Other definitions for ark that I've seen before include "Rescue vessel" , "Animal rescue transport" , "Noah's craft" , "old vessel" , "Sacred chest" .)