Feeling conveyed that is not heartless (8)
I believe the answer is:
sentient
'feeling' is the definition.
('sentient' can be a synonym of 'feeling')
'conveyed that is not heartless' is the wordplay.
'conveyed' becomes 'sent' (sending is a kind of conveying).
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'heartless' says to hollow out the word (remove centre letters).
'not' with its middle removed is 'nt'.
'sent'+'ie'+'nt'='SENTIENT'
(Other definitions for sentient that I've seen before include "Endowed with feeling and consciousness" , "Able to perceive or feel things" , "Having feelings" , "Capable of feeling and perceiving things" , "Feeling, conscious" .)