Kiln’s broken connection (4)
I believe the answer is:
link
'connection' is the definition.
(link is a kind of connection)
'kiln's broken' is the wordplay.
'broken' is an anagram indicator.
'kiln' anagrammed gives 'LINK'.
(Other definitions for link that I've seen before include "Connecting part" , "One ring or loop of a chain" , "Means of connection between things" , "Tie-up" , "A chain is as strong as its weakest one" .)