Obvious liar about to cut Chopin composition, Zeus's lover (9)
I believe the answer is:
pinocchio
'obvious liar' is the definition.
(character whose nose grows when he lies)
'about to cut chopin composition zeus's lover' is the wordplay.
'about' becomes 'c' (abbreviation for 'circa'**).
'to cut' is an insertion indicator.
'composition' is an anagram indicator.
'zeus's lover' becomes 'io' (Io was a lover of Zeus in Greek myth).
'chopin' with letters rearranged gives 'pinoch'.
'c' placed within 'pinoch' is 'pinocch'.
'pinocch'+'io'='PINOCCHIO'
(Other definitions for pinocchio that I've seen before include "Nose-growing puppet" , "Fairytals puppet who became a boy" , "Wooden puppet, prone to lying" , "Wooden puppet, brought alive" , "dishonest puppet" .)