Passage connecting successfully into barrels in Kent town (9,5)
I believe the answer is:
tunbridge wells
'kent town' is the definition.
'passage connecting successfully into barrels' is the wordplay.
'passage connecting' becomes 'bridge' (as in a musical bridge).
'successfully' becomes 'well' (I've seen this in other clues).
'into' is an insertion indicator.
'barrels' becomes 'tuns' (tun is a kind of barrel).
'bridge'+'well'='bridgewell'
'bridgewell' going into 'tuns' is 'TUNBRIDGE WELLS'.
'in' acts as a link.
(Other definitions for tunbridge wells that I've seen before include "Disgusted posts from here" , "correspondents here outraged?" , "Kentish town" .)