Asian girl visiting W African state endlessly (7)
I believe the answer is:
bengali
'asian' is the definition.
(native of Bengal)
'girl visiting w african state endlessly' is the wordplay.
'girl' becomes 'gal' (synonyms).
'visiting' means one lot of letters goes inside another.
'w african state' becomes 'Benin' (West African country).
'endlessly' means to remove the last letter.
'benin' with its final letter taken off is 'beni'.
'gal' placed within 'beni' is 'BENGALI'.
(Other definitions for bengali that I've seen before include "Language of Bangladesh and northeast India" , "Native of Calcutta region" , "Asian language" , "may be Indian" , "From Dhaka or Kolkata, perhaps" .)