Bound to be exhausted, disheartened (4)
I believe the answer is:
tied
'bound' is the definition.
('tie' can be a synonym of 'bind')
'exhausted disheartened' is the wordplay.
'exhausted' becomes 'tired' ('tire' can be a synonym of 'exhaust').
'disheartened' suggests removing the centre.
'tired' with its middle taken out is 'TIED'.
'to be' is the link.
(Other definitions for tied that I've seen before include "Drawn" , "In no-win situation" , "(Of pub) controlled by a brewery" , "Made into a knot" , "limited" .)