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 with a rapid darting motion", "Dart off", "Depart quickly (does not contain H)", "Leave quickly", "Move rapidly" and "Skedaddle".)