… back to pursue quiet ways (7)
I believe the answer is:
streets
'ways' is the definition.
(street is a kind of way)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for streets that I've seen before include "Built-up roads" , "Ways" , "significantly ahead?" , "City thoroughfares" , "Town thoroughfares" .)