A dry one around Greek region (6)
I believe the answer is:
attica
'greek region' is the definition.
(I've seen this before)
'a dry one around' is the wordplay.
'dry' becomes 'tt' (abbreviation for teetotal).
'one' becomes 'i' (Roman numeral).
'around' becomes 'ca' (circa**).
'a'+'tt'+'i'+'ca'='ATTICA'
(Other definitions for attica that I've seen before include "Greek district" , "Greek region that includes Athens" , "historic Greek region" , "a Greek city" , "In ancient times the territory of Athens" .)