A desert area in eastern French region (9)
I believe the answer is:
aquitaine
'french region' is the definition.
(Aquitaine is an example)
'a desert area in eastern' is the wordplay.
'desert' becomes 'quit' (I've seen this before).
'area' becomes 'a' (maths abbreviation).
'eastern' becomes 'e'.
'a'+'quit'+'a'+'in'+'e'='AQUITAINE'
(Other definitions for aquitaine that I've seen before include "Formerly English region of France" , "somewhere in France" , "part of France" , "historical region of France" , "Region in SW France" .)