Foremost Irish girl gets discharge, when rejected (7)
I believe the answer is:
supreme
'foremost' is the definition.
(thesaurus)
'irish girl gets discharge when rejected' is the wordplay.
'irish girl' becomes 'Emer' (Irish name).
'gets' is a charade indicator (letters next to each other).
'discharge' becomes 'pus' (I've seen this before).
'when rejected' shows that the letters should be reversed in order.
'emer'+'pus'='emerpus'
'emerpus' reversed gives 'SUPREME'.
(Other definitions for supreme that I've seen before include "Greatest, highest in excellence" , "Creamy sauce" , "Best of all" , "Cardinal, foremost" , "God" .)