Adult in Neath might be Greek (8)
I believe the answer is:
athenian
'greek' is the definition.
(I know that Athenian is a type of greek)
'adult in neath might be' is the wordplay.
'adult' becomes 'a' (abbreviation).
'might be' indicates an anagram.
'in'+'neath'='inneath'
'inneath' anagrammed gives 'thenian'.
'a'+'thenian'='ATHENIAN'
(Other definitions for athenian that I've seen before include "City dweller" , "One from the Greek capital" , "Is the Greek in AA then?" , "Native of Grecian capital" , "Citizen of Greece's capital" .)