Middle East - not possibly in the Birmingham area! (5)
I believe the answer is:
aston
'birmingham area' is the definition.
'aston' can be an answer for 'area' (I have seen 'Area of Birmingham ' mean 'aston' so perhaps 'area' could also mean 'aston'). I'm unsure of the 'birmingham' bit.
'middle east not possibly' is the wordplay.
'middle' says to take the centre.
'possibly' indicates an anagram.
The centre of 'east' is 'as'.
'not' anagrammed gives 'ton'.
'as'+'ton'='ASTON'
'in the' is the link.
Can you help me to learn more?
(Other definitions for aston that I've seen before include "A Birmingham university" , "Area of Birmingham" , "Premiership FC" , "- Villa, football club" , "part of Birmingham" .)