Greek character first in queue as barbarian (10)
I believe the answer is:
philistine
'barbarian' is the definition.
(thesaurus)
'greek character first in queue' is the wordplay.
'greek character' becomes 'phi' (letter from the Greek alphabet).
'first' becomes 'ist' (**).
'in' means one lot of letters goes inside another.
'queue' becomes 'line' (I've seen this before).
'ist' put into 'line' is 'listine'.
'phi'+'listine'='PHILISTINE'
'as' is the link.
(Other definitions for philistine that I've seen before include "Tasteless" , "One indifferent to culture" , "One hostile to culture" , "Someone indifferent to culture and the arts" , "one who's lowbrow?" .)