National idioms a woman found going over a chap’s manuscript (9)

'national idioms' is the definition.
(typically Irish words or phrases)

'a woman found going over a chap's manuscript' is the wordplay.
'a woman' becomes 'iris' ().
'found going over' is a charade indicator (letters next to each other) (in a down clue, some letters go above others).
'a chap's' becomes 'his' (possessive pronoun for a male or 'chap').
'manuscript' becomes 'ms' (abbreviation for manuscript).
'iris'+'his'+'ms'='IRISHISMS'