Fasten case? Not quite (6)
I believe the answer is:
attach
'fasten' is the definition.
(thesaurus)
'case? not quite' is the wordplay.
'case?' becomes 'attache' (attache is a kind of case).
'not quite' means to remove the last letter.
'attache' with its last letter taken away is 'ATTACH'.
(Other definitions for attach that I've seen before include "Add or join to" , "Tag on" , "Join; seize (legal)" , "'Affix, fasten (6)'" , "Document carriers" .)