Country — popular destination in Asia, primarily (5)
I believe the answer is:
india
'country' is the definition.
(India is an example)
'popular destination in asia primarily' is the wordplay.
'popular' becomes 'in'.
'primarily' indicates taking the first letters.
The first letters of 'destination in asia' is 'dia'.
'in'+'dia'='INDIA'
(Other definitions for india that I've seen before include "Republic in south Asia" , "New Delhi is its capital" , "Asian sub-continent" , "home to her Mumbai family" , "Gandhi's country" .)