Woman born in People's Assembly (8)
I believe the answer is:
penelope
'woman' is the definition.
'born in people's assembly' is the wordplay.
'born' becomes 'ne' ('born' in French - used to indicate a birth name).
'in' means one lot of letters goes inside another.
'assembly' indicates an anagram.
'people' with letters rearranged gives 'pelope'.
'ne' placed into 'pelope' is 'PENELOPE'.
(Other definitions for penelope that I've seen before include "Odysseus's wife" , "lady" , "Ulysses' faithful wife" , "girl" , "Girl's name" .)