Longman Dictionary of Contemporary English
Wiktionary
n. increased traffic due to the number of parents taking or collecting their children to and from school by car.
Wikipedia
Usage examples of "school run".
There might be a school run by nuns or something that would take them in.
Kooralbyn International School, built in 1985, is an unusual concept, an independent, non-government, non-profit, privately owned school run by a board of governors.
Because the daily paper doesn't get to Scardale till lunchtime and Hawkin likes a paper with his breakfast, the newsagent at Longnor leaves an Evening News in the mailbox at the end of the lane every morning and whoever does the school run drops it off at the manor afterwards.
She thought of Stella, far across the continent, wasting her time in a school run by bigots.
The ones I committed when I was twelve and thirteen that inspired my parents, even though they were far, far, from prosperous, to decide that I belonged in a girls' boarding school run by nuns until I graduated from high school.
There was a school run by an old Anglican priest and a white woman whose face had been half-destroyed by the sun.