A Bible kept in rigorous university (7)
I believe the answer is:
harvard
'university' is the definition.
(Harvard is an example)
'a bible kept in rigorous' is the wordplay.
'bible' becomes 'rv' (Revised Version, revision of King James Bible).
'kept in' means one lot of letters goes inside another.
'rigorous' becomes 'hard' ('hard' can be similar in meaning to 'rigorous').
'a'+'rv'='arv'
'arv' going within 'hard' is 'HARVARD'.
(Other definitions for harvard that I've seen before include "US university, founded 1636" , "Member of the 11 at Cambridge, Massachusetts" , "American university" , "Ivy-league university" , "Oldest US university" .)