Sway from side to side on street walk (6)

I believe the answer is:
stroll
'walk' is the definition.
(stroll is a kind of walk)
'sway from side to side on street' is the wordplay.
I cannot quite understand how this works, but
'sway' could be 'roll' (I've seen this in another clue) and 'roll' is found within the answer.
'street' could be 'st' (abbreviation) and 'st' is present in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for stroll that I've seen before include "A pleasant and leisurely walk" , "Amble or ramble" , "Constitutional" , "cinch" , "Amble along" .)
