Claim to replace women in deep admiration for position at Oxford? (13)
I believe the answer is:
professorship
'for position at oxford?' is the definition.
(Oxford is a university)
'claim to replace women in' is the wordplay.
'claim' becomes 'profess' (professing is a kind of claiming).
'to replace women' becomes 'ors' (I can't justify this - if you can you should believe this answer much more).
'in' becomes 'hip' (both can mean fashionable).
'profess'+'ors'+'hip'='PROFESSORSHIP'
'deep admiration' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Other definitions for professorship that I've seen before include "Academic position" , "University post" , "University chair" , "Academic post" .)