Woman, North American, to overlook losing time (5)
I believe the answer is:
naomi
'woman' is the definition.
'north american to overlook losing time' is the wordplay.
'north american' becomes 'na'.
'to overlook' becomes 'omit' ('omit' can be a synonym of 'overlook').
'losing' is a deletion indicator.
'time' becomes 't'.
'omit' with 't' taken out is 'omi'.
'na'+'omi'='NAOMI'
(Other definitions for naomi that I've seen before include "woman's name" , "Biblical mother-in-law of Ruth" , "Biblical woman" , "Relative of Ruth" , "Girl" .)