On his first day as CEO of Cisco, in July 2015, Chuck Robbins appointed a tech veteran, Zorawar “Biri” Singh, as CTO. It turned out to be a contentious appointment, irritating Mr. Robbins’ predecessor John Chambers, four senior executives close to Mr. Chambers as well as Cisco’s sales team, in part because of differences over Cisco’s technical strategy. The four ended up quitting a year later. Mr. Singh himself left after 15 months in the job.

The previously unreported tensions over Mr. Singh’s hiring highlights the challenges facing Mr. Robbins, a 20-year old veteran of Cisco who leapfrogged more senior people at the company to snare the top job. While similar in many ways to Mr. Chambers—both are gregarious salespeople who grew up in the South—Mr. Robbins has departed from Mr. Chambers’ strategy in steering Cisco through challenging times. And he has had to do so while Mr. Chambers is looking over his shoulder, as executive chairman, remaining closely involved.