A revolver, possibly, disheartens the doctor (4)
I believe the answer is:
door
'a revolver possibly' is the definition.
(I know that revolver is a type of Door)
'disheartens the doctor' is the wordplay.
'disheartens' suggests removing the centre (I've seen 'dishearten' mean this).
'doctor' with its middle removed is 'DOOR'.
(Other definitions for door that I've seen before include "Portal" , "Entrance way" , "Moveable structure at an entrance" , "Entrance to room, house etc" , "Usual entrance" .)