Old city flourishing with distinguished artist (7)
I believe the answer is:
palmyra
'old city' is the definition.
(ancient Syrian city)
'flourishing with distinguished artist' is the wordplay.
'flourishing' becomes 'palmy' (synonyms).
'with' says to put letters next to each other.
'distinguished artist' becomes 'RA' (member of the Royal Academy).
'palmy'+'ra'='PALMYRA'
(Other definitions for palmyra that I've seen before include "Ancient city of 5 dn" , "Ancient city in Syria" , "Historic city in Syria" , "One may produce toddy" , "overseas branches" .)