Single chap from east cut by Oscar's woman (5)
I believe the answer is:
naomi
'woman' is the definition.
'single chap from east cut by oscar's' is the wordplay.
'single' becomes 'I' (one).
'chap' becomes 'man' (chap can mean a man).
'from east' is a reversal indicator (letters written right to left or 'east to west').
'cut by' indicates putting letters inside (some letters cut into others).
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'i'+'man'='iman'
'iman' in reverse letter order is 'nami'.
'nami' placed around 'o' is 'NAOMI'.
(Other definitions for naomi that I've seen before include "Biblical character" , "OT female" , "Mother-in-law of Ruth (Bible)" , "woman in the Bible" , "Girl's name, meaning "pleasant"" .)