Shorten a connection (7)
I believe the answer is:
abridge
'shorten' is the definition.
(synonyms)
'a connection' is the wordplay.
'connection' becomes 'bridge' (bridge is a kind of connection).
'a'+'bridge'='ABRIDGE'
(Other definitions for abridge that I've seen before include "Shorten, a book say, without losing the sense" , "Big read (anag) - shorten text" , "trim" , "Concentrate" , "Condense, summarise" .)