Crossword Genius

Sway from side to side on street walk (6)

Ross

I believe the answer is:

stroll

I'm a little stuck... Click here to teach me more about this clue!

'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" .)

I've seen this clue in The Times.
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