Note heartless opponent finding monument? (8)
I believe the answer is:
memorial
'monument?' is the definition.
('memorial' can be a synonym of 'monument')
'note heartless opponent' is the wordplay.
'note' becomes 'memo' (memo is a kind of note).
'heartless' suggests removing the centre.
'opponent' becomes 'rival' (I've seen this in another clue).
'rival' with its middle taken out is 'rial'.
'memo'+'rial'='MEMORIAL'
'finding' is the link.
(Other definitions for memorial that I've seen before include "Serving to commemorate the dead" , "Monument such as the Cenotaph" , "Relic, monument" , "Statue or monument that commemorates" , "Monument to past events" .)