David's wife in university city, the woman with arts degree (9)
I believe the answer is:
bathsheba
'david's wife' is the definition.
(wife of King David in the Bible)
'university city the woman with arts degree' is the wordplay.
'university city' becomes 'Bath' (site of the University of Bath).
'the woman' becomes 'she' ('she' refers to a woman).
'with' says to put letters next to each other.
'arts degree' becomes 'BA' (Bachelor of Arts).
'bath'+'she'+'ba'='BATHSHEBA'
'in' acts as a link.
(Other definitions for bathsheba that I've seen before include "biblical character" , "David's wife" , "woman once exploited" , "OT character" , "Wife of Uriah" .)