Carla touring East Asian country (6)
I believe the answer is:
brunei
'asian country' is the definition.
(country in Asia)
'carla touring east' is the wordplay.
'carla' becomes 'Bruni' (Carla Bruni).
'touring' indicates putting letters inside (touring can mean going round).
'east' becomes 'e' (abbreviation).
'bruni' placed around 'e' is 'BRUNEI'.
(Other definitions for brunei that I've seen before include "Eastern land" , "Rich sultanate in the South China Sea" , "Muslim state" , "Commonwealth member" , "Ill" .)