West Asian monarchy captures rebel leader in this building (7)
I believe the answer is:
turkish
'west asian' is the definition.
(I know this)
'monarchy captures rebel leader in this building' is the wordplay.
'monarchy' becomes 'uk' (the United Kingdom is a monarchy).
'captures' indicates putting letters inside.
'leader' suggests taking the first letters.
'in' is an insertion indicator.
'building' indicates an anagram.
The initial letter of 'rebel' is 'r'.
'uk' going around 'r' is 'urk'.
'this' anagrammed gives 'tish'.
'urk' inserted inside 'tish' is 'TURKISH'.
(Other definitions for turkish that I've seen before include "-- bath; -- delight" , "Does ski hurt this nationality?" , "Nationality of a citizen of Ankara" , "From Constantinople, perhaps" , "Eg, native to Ankara" .)