Girlfriend storing one volume in case (6)
I believe the answer is:
dative
'case' is the definition.
(dative is a kind of case)
'girlfriend storing one volume' is the wordplay.
'girlfriend' becomes 'date' (I've seen this in other clues).
'storing' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'volume' becomes 'v'.
'i'+'v'='iv'
'date' enclosing 'iv' is 'DATIVE'.
'in' acts as a link.
(Other definitions for dative that I've seen before include "'To' case (grammar)" , "Grammatical case" .)