Australian prime minister's backed out (6)
I believe the answer is:
asleep
'out' is the definition.
(out can mean unconscious or asleep)
'australian prime minister's backed' is the wordplay.
'australian' becomes 'A' (common abbreviation).
'prime minister's' becomes 'peel's' (Robert Peel).
'backed' shows that the letters should be reversed in order.
'peels' written backwards gives 'sleep'.
'a'+'sleep'='ASLEEP'
(Other definitions for asleep that I've seen before include "Napping" , "Please be at rest (6)." , "Dead to the world" , "Having forty winks" , "not paying attention" .)