Tory takes a long time to shut up (4)
I believe the answer is:
cage
'shut up' is the definition.
(thesaurus)
'tory takes a long time' is the wordplay.
'tory' becomes 'c'.
'takes' is a charade indicator (letters next to each other).
'a long time' becomes 'age' ('age' can be a synonym of 'long time'**).
'c'+'age'='CAGE'
'to' is the link.
(Other definitions for cage that I've seen before include "In places squirrel's nest" , "Barred container" , "Eg, aviary" , "Enclosure made from metal bars" , "Confine -- US composer, d. 1992" .)