Given heart transplant, start living (5)
I believe the answer is:
being
'start living' is the definition.
'being' can be an answer for 'living' (I've seen this in another clue). I am not sure about the 'start' bit.
'given heart transplant' is the wordplay.
'given' becomes 'bein' (I can't justify this - if you can you should believe this answer much more).
'heart' says to take the centre.
'transplant' becomes 'homograft' (I've seen this before).
The centre of 'homograft' is 'g'.
'bein'+'g'='BEING'
(Other definitions for being that I've seen before include "Person" , "Living thing" , "A matter of 9 in the play" , "substance" , "Existence" .)