Moved quickly as one dared around the East End (6)
I believe the answer is:
darted
'moved quickly' is the definition.
(I've seen this in another clue)
'one dared around the east end' is the wordplay.
'around' means one lot of letters goes inside another.
'end' says to take the final letters.
The final letter of 'east' is 't'.
'dared' placed around 't' is 'DARTED'.
'as' acts as a link.
(Other definitions for darted that I've seen before include "Moved suddenly and rapidly" , "Moved rapidly and lightly" , "Dashed, flitted" , "Dashed on the Dublin transport system?" , "Moved quickly and suddenly" .)