Relative with a universal set of books (4)
I believe the answer is:
aunt
'relative' is the definition.
(aunt is a kind of relative)
'with a universal set of books' is the wordplay.
'with' means one lot of letters go next to another.
'universal' becomes 'u'.
'set of books' becomes 'NT' (New Testament).
'a'+'u' is 'au'.
'au'+'nt'='AUNT'
(Other definitions for aunt that I've seen before include "Close relative" , "Tuna for the odd relative" , "Tuna (anag.)" , "Parent's sister" , "Uncle's wife" .)