Nigerian university admitting French or German woman (8)
I believe the answer is:
hausfrau
'german woman' is the definition.
(term for a German housewife)
'nigerian university admitting french' is the wordplay.
'nigerian' becomes 'Hausa' (many of the Hausa people live in Nigeria).
'university' becomes 'U' (abbreviation for university).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'french' becomes 'fr' (abbreviation).
'hausa'+'u'='hausau'
'hausau' enclosing 'fr' is 'HAUSFRAU'.
'or' acts as a link.
(Other definitions for hausfrau that I've seen before include "A German married woman working in the home" , "(For a German) 'er indoors" , "Bonn homemaker" , "wife at home" .)