Stops buffs heading off in pursuit of Australian book (9)

'stops' is the definition.
(to abolish is to ban or stop)

'buffs heading off in pursuit of australian book' is the wordplay.
'buffs' becomes 'polishes' (to buff is to polish or clean).
'heading off' means to remove the first letter.
'in pursuit of' is a charade indicator (letters next to each other).
'australian' becomes 'A'.
'book' becomes 'b' (abbreviation for book).
'polishes' with its initial letter removed is 'olishes'.
'a'+'b'='ab'
'olishes' put after 'ab' is 'ABOLISHES'.