Listen to organist's last organ (5)
I believe the answer is:
heart
'organ' is the definition.
(the heart is an organ of the body)
'listen to organist's last' is the wordplay.
'listen to' becomes 'hear' (to hear something is to listen to it).
'last' indicates one should take the final letters.
The last letter of 'organist' is 't'.
'hear'+'t'='HEART'
(Other definitions for heart that I've seen before include "Middle" , "Not a club" , "Kernel" , "Vital part" , "the name of a prison in Midlothian!" .)