Greek lost in Antioch beginning to revive within (10)
I believe the answer is:
corinthian
'greek' is the definition.
(Corinthian is an example)
'lost in antioch beginning to revive within' is the wordplay.
'lost' indicates an anagram.
'beginning to' indicates taking the first letters.
'within' means one lot of letters goes inside another.
The initial letter of 'revive' is 'r'.
'in'+'antioch'='inantioch'
'inantioch' anagrammed gives 'cointhian'.
'cointhian' enclosing 'r' is 'CORINTHIAN'.
(Another definition for corinthian that I've seen is " Recipient of Paul's letter".)