Note by Irishwoman failing to finish biographical sketch (6)
I believe the answer is:
memoir
'biographical sketch' is the definition.
(I've seen this before)
'note by irishwoman failing to finish' is the wordplay.
'note' becomes 'memo' (a memo is a short note).
'by irishwoman failing' becomes 'ir' (I am not sure about this - if you are sure you should believe this answer much more).
'to finish' says to put letters next to each other (some letters go after or 'finish' others).
'memo'+'ir'='MEMOIR'
Can you help me to learn more?
(Other definitions for memoir that I've seen before include "Biographical account" , "Biographical sketch" , "Written account of events in one's life" , "Personal life story" , "Personal history" .)