Reportedly moved fast in Tube? (4)
I believe the answer is:
flue
'tube?' is the definition.
(I've seen this before)
'reportedly moved fast' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'moved fast' becomes 'flew' (I've seen this in another clue).
'flew' sounds like 'FLUE'.
'in' is the link.
(Other definitions for flue that I've seen before include "Chimney-shaft" , "Fume vent" , "Fuel (anag.)" , "Escape" , "smoky passage" .)