Liberal ambience is the making of a girl (5)
I believe the answer is:
laura
'a girl' is the definition.
(girl's name)
'liberal ambience' is the wordplay.
'liberal' becomes 'l' (abbreviation).
'ambience' becomes 'aura' (I've seen this before).
'l'+'aura'='LAURA'
'is the making of' is the link.
(Other definitions for laura that I've seen before include "Girl's name" , "Petrarch loved her" , "US First Lady" , "girl" , "__ Ashley, Welsh fashion and textile designer, d. 1985" .)