A living thing's heart perhaps is beginning to move (8)
I believe the answer is:
organism
'a living thing's' is the definition.
('organism' can be a synonym of 'living thing')
'heart perhaps is beginning to move' is the wordplay.
'heart perhaps' becomes 'organ' (heart is a kind of organ).
'beginning to' indicates taking the first letters.
The first letter of 'move' is 'm'.
'organ'+'is'+'m'='ORGANISM'
(Other definitions for organism that I've seen before include "Individual life form" , "Living animal or plant" , "individual creation" , "Something alive" , "Living animal or vegetable" .)