Love god has sore back (4)
I believe the answer is:
eros
'love god' is the definition.
(Greek god of love)
'sore back' is the wordplay.
'back' says the letters should be written in reverse.
'sore' in reverse letter order is 'EROS'.
'has' is the link.
(Other definitions for eros that I've seen before include "One worshipped" , "Goddess" , "Group of instincts" , "God of love; life instinct (Freud)" , "Winged god of love" .)