Run with a cry into the street (5)
I believe the answer is:
Here is my best explanation:
'run' is the definition.
'a cry into the street' is the subsidiary indication.
'a cry' becomes 'coo' (coo is a kind of cry**).
'into' indicates putting letters inside.
'the street' becomes 'st'.
'coo' inserted into 'st' is 'scoot'.
'with' is the link.
(Other definitions for scoot that I've seen before include "Move rapidly", "Move with a rapid darting motion", "hurry", "Dart off", "Depart quickly (does not contain H)", "Leave quickly", "Skedaddle" and "hightail it".)