Debauchee having left island, knight Edward VII embraces? (9)
I believe the answer is:
libertine
'debauchee' is the definition.
(I know that debauchee can be written as libertine)
'left island knight edward vii embraces?' is the wordplay.
'left' becomes 'l' (common abbreviation).
'island' becomes 'i' (geographical abbreviation).
'knight' becomes 'n' (chess abbreviation).
'edward vii' becomes 'bertie' (nickname of Edward VII, born Albert).
'embraces?' indicates putting letters inside.
'n' inserted within 'bertie' is 'bertine'.
'l'+'i'+'bertine'='LIBERTINE'
'having' acts as a link.
(Other definitions for libertine that I've seen before include "Say, Don Giovanni" , "of roues" , "Don Giovanni perhaps" , "Person who live immorally - sounds free" , "Debauchee" .)