It's Sooty and Sweep's workplace? (7)
I believe the answer is:
chimney
I believe this is a double definition.
'it's sooty' is the first definition.
(I know that chimney are often sooty)
'sweep's workplace?' is the second definition.
(I know that chimney sweeps work in chimneys)
'and' is the link.
(Other definitions for chimney that I've seen before include "A cleft for climbing" , "Father Christmas's entry?" , "funnel" , "Flue" , "Smoke outlet" .)