First public performance (8)
'first public performance' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for premiere that I've seen before include "First screening" , "significant performance" , "First showing of play or film" , "First ever public performance" , "Opening night" .)
(Other definitions for debut that I've seen before include "Tubed (anag.)" , "First appearence as of society girl" , "Beginning, first performance" , "entrance" , "Introduction" .)