Byzantine Empire's concerning debut (8)
I believe the answer is:
premiere
'debut' is the definition.
(thesaurus)
'byzantine empire's concerning' is the wordplay.
'byzantine' indicates an anagram (byzantine means complex or confusing).
'concerning' becomes 're' (both can mean on a particular topic).
'empire' anagrammed gives 'premie'.
'premie'+'re'='PREMIERE'
(Other definitions for premiere that I've seen before include "First showing of play or film" , "Leading lady" , "First screening" , "First ever public performance" , "Play's first public performance" .)