Puncture cut short a woman taking in Irish county (10)
I believe the answer is:
lancashire
'county' is the definition.
(English county)
'puncture cut short a woman taking in irish' is the wordplay.
'puncture' becomes 'lance'.
'cut short' means to remove the last letter.
'woman' becomes 'she' (**).
'taking in' indicates putting letters inside.
'irish' becomes 'ir' (abbreviation).
'lance' with its final letter removed is 'lanc'.
'she' going around 'ir' is 'shire'.
'lanc'+'a'+'shire'='LANCASHIRE'
(Other definitions for lancashire that I've seen before include "North-Western county" , "Crumbly white cheese" , "Stew from the Northwest" , "County of NW England" , "Part of country" .)