One out of shape, losing heart (4)
I believe the answer is:
unit
'one' is the definition.
('unit' can be a synonym of 'one')
'out of shape losing heart' is the wordplay.
'out of shape' becomes 'unfit' (I've seen this before).
'losing heart' suggests removing the centre.
'unfit' with its middle removed is 'UNIT'.
(Other definitions for unit that I've seen before include "Army division" , "Entity making up part of a whole" , "Body of soldiers" , "Individual thing; one" , "Element or part" .)