Well-mannered chap left beyond the outskirts of Eastbourne (7)
I believe the answer is:
genteel
'well-mannered' is the definition.
(thesaurus)
'chap left beyond the outskirts of eastbourne' is the wordplay.
'chap' becomes 'gent' (I've seen this in other clues**).
'left' becomes 'l' (common abbreviation).
'beyond' is a charade indicator (letters next to each other).
'the outskirts of' says to hollow out the word (remove centre letters).
'eastbourne' with its middle taken out is 'ee'.
'l' put after 'ee' is 'eel'.
'gent'+'eel'='GENTEEL'
(Other definitions for genteel that I've seen before include "Well mannered" , "Courteous, well-bred" , "Affectedly polite and refined" , ""Refayned"" , "Overly polite or refined" .)