Madeira question not constructed in Middle East (4)
I believe the answer is:
iraq
'in middle east' is the definition.
('Iraq' is part of 'middle east')
'madeira question not constructed' is the wordplay.
'question' becomes 'q'.
'not' indicates named letters should be taken away.
'constructed' becomes 'made' ('make' can be a synonym of 'construct').
'madeira'+'q'='madeiraq'
'madeiraq' with 'made' removed is 'IRAQ'.
(Other definitions for iraq that I've seen before include "war-torn nation" , "Middle-Eastern state" , "Where no WMD were found" , "Baghdad's country" , "Putter, perhaps" .)