Elicit approval in first woman (5)
I believe the answer is:
evoke
'elicit' is the definition.
('evoke' can be a synonym of 'elicit')
'approval in first woman' is the wordplay.
'approval' becomes 'ok' (OK is an example).
'in' means one lot of letters goes inside another.
'first woman' becomes 'eve' (I've seen this before**).
'ok' inserted within 'eve' is 'EVOKE'.
(Other definitions for evoke that I've seen before include "Prompt" , "Summon up" , "Conjure up" , "Elicit (a response)" , "Raise" .)