Eventually accepting heartless act is personal (8)
I believe the answer is:
intimate
'personal' is the definition.
(synonyms)
'eventually accepting heartless act' is the wordplay.
'eventually' becomes 'intime' (synonyms).
'accepting' is an insertion indicator (inserted letters are accepted).
'heartless' suggests removing the centre.
'act' with its middle taken out is 'at'.
'intime' going around 'at' is 'INTIMATE'.
'is' is the link.
(Other definitions for intimate that I've seen before include "Private and personal like close acquaintanceship" , "Hint to a familiar friend" , "Tip off" , "Bosom" , "Personal - hint - friend" .)