Father backed a horse — he's a heathen (5)
I believe the answer is:
pagan
'heathen' is the definition.
(both can mean an irreligious person)
'father backed a horse' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'backed' shows that the letters should be reversed in order.
'a horse' becomes 'nag' (term for an old horse).
'nag' reversed gives 'gan'.
'pa'+'gan'='PAGAN'
'he's a' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for pagan that I've seen before include "One who does not acknowledge a god" , "Person without any conventional religion" , "Non-mainstream religious believer" , "advocate of pleasures" , "Infidel" .)