Observing nought after losing heart (6)
I believe the answer is:
noting
'observing' is the definition.
('note' can be a synonym of 'observe')
'nought after losing heart' is the wordplay.
'nought' becomes 'nothing' (synonyms).
'after losing heart' suggests removing the centre.
'nothing' with its centre removed is 'NOTING'.
(Other definitions for noting that I've seen before include "Making brief record as memory aid" , "Observing and jotting down" , "Observing or taking down" , "Paying close attention to something" , "Seeing" .)