Asian country encompassing a new state (7)
I believe the answer is:
indiana
'state' is the definition.
(Indiana is an example)
'asian country encompassing a new' is the wordplay.
'asian country' becomes 'india' (India is an example).
'encompassing' indicates putting letters inside.
'a new' becomes 'an' (I've seen this in other clues).
'india' enclosing 'an' is 'INDIANA'.
(Other definitions for indiana that I've seen before include "--- Jones, Harrison Ford film character" , "part of USA" , "Vice President Pence's state" , "US Midwest state" , "American state" .)