Measure of cloth needed by a lady (4)
I believe the answer is:
ella
'lady' is the definition.
(woman's name)
'measure of cloth needed by a' is the wordplay.
'measure of cloth' becomes 'ell' (historical unit of measurement for fabric).
'needed by' means one lot of letters go next to another.
'ell'+'a'='ELLA'
(Other definitions for ella that I've seen before include "Miss" , "Ms Fitzgerald" , "---- Fitzgerald, 'Queen of Jazz'" , "Woman" , "Diminutive of Eleanor" .)