I dashed in to embrace a native of Western Asia (7)
I believe the answer is:
iranian
'native of western asia' is the definition.
'i dashed in to embrace a' is the wordplay.
'dashed' becomes 'ran'.
'to embrace' indicates putting letters inside.
'in' enclosing 'a' is 'ian'.
'i'+'ran'+'ian'='IRANIAN'
(Other definitions for iranian that I've seen before include "Modern Persian language" , "Eg, native of Teheran" , "Eg, native of Tehran" , "One from Isfahan" , "from the Middle East" .)