Fasten on to bag (5)
I believe the answer is:
catch
I believe this is a double definition.
'fasten' is the first definition.
(thesaurus)
'to bag' is the second definition.
('catch' can be a synonym of 'bag')
'on' is the link.
(Other definitions for catch that I've seen before include "Fly in the ointment" , "Desirable husband; unforeseen problem" , "Intercept and hold" , "Hidden problem; trap" , "problem in small print?" .)