Health resort and art complex in ancient Greece (6)
I believe the answer is:
sparta
'in ancient greece' is the definition.
(I've seen this before)
'health resort and art complex' is the wordplay.
'health resort' becomes 'spa' (spa can mean a health resort).
'and' means one lot of letters go next to another.
'complex' indicates anagramming the letters.
'art' is an anagram of 'rta'.
'spa'+'rta'='SPARTA'
(Other definitions for sparta that I've seen before include "Ancient Greek city known for warlike spirit" , "Enemy of Athens?" , "Ancient Greek city state" , "Ancient Greek city noted for tough citizens" , "austere place" .)