Foreign farewell (5)
(Other definitions for adios that I've seen before include "Goodbye (Spanish)" , "Bye-bye (amigo)" , "Spanish farewell" , "Goodbye, amigo" , "So long, amigo" .)
'foreign farewell' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for adieu that I've seen before include "I'm going" , "Farewell, ami!" , "A valediction" , "Cheerio" , "Leave" .)