Girl touring island, an American state (9)
I believe the answer is:
louisiana
'american state' is the definition.
(Louisiana is an example)
'girl touring island an' is the wordplay.
'girl' becomes 'louisa' ().
'touring' is an insertion indicator (tour can mean to go around).
'island' becomes 'i' (geographical abbreviation).
'i'+'an'='ian'
'louisa' placed around 'ian' is 'LOUISIANA'.
(Other definitions for louisiana that I've seen before include "State named for French king" , "American state, capital Baton Rouge" , "US state, capital Baton Rouge" , "Southern United State on the Gulf of Mexico" , "that's near Mississippi" .)