Move swiftly into the westbound autostrada (4)
I believe the answer is:
dart
'move swiftly' is the definition.
(to dart is to move quickly)
'into the westbound autostrada' is the wordplay.
'the westbound' is a reversal indicator (letters written from right to left).
'into' indicates the answer is hidden within the clue.
'trad' can be found hidden inside 'autostrada'.
'trad' in reverse letter order is 'DART'.
(Other definitions for dart that I've seen before include "Arrow; dash" , "flash" , "quarrel" , "Move quickly and suddenly" , "Devon river - bound - race" .)