Wiktionary
run around after
vb. (context idiomatic transitive English)To spend a lot of time doing things for another person or group of people. Often used when that person could reasonably do the things for themselves.
Usage examples of "run around after".
His life had been fifteen years of luxury, of staff existing solely to run around after him, of any material possession he wanted a single phone call away.
Am I supposed to run around after my clients begging them to let me help them?