Ynon Kreiz has made play his work. As the chief executive of Mattel , the 76-year-old toy company, Mr. Kreiz oversees Barbie dolls, Hot Wheels cars and other children’s products that have filled toy shelves for decades—and this past year, served as pandemic lifesavers for parents entertaining bored kids stuck at home.

These are some of the most iconic brands in the world. Making any changes to such beloved brands means balancing the new with the nostalgic. But now that the U.S. is reopening and quarantines are being lifted, Mr. Kreiz faces a fresh challenge: Adjusting to the new expectations and desires of consumers shaped by 14 months of seismic changes to work-life balance and nationwide calls for better inclusivity and representation in the broader culture. Add it to the list of changes Mr. Kreiz must bring to a company that had seen lower sales—and significant executive turnover—before he assumed the CEO job in April 2018. Since he took over, Mattel has seen three consecutive quarters of growing market share, and its stock price has returned to levels not seen since the summer of 2017.

A veteran of the tech world, Mr. Kreiz says he wants to leverage the iconic brands under the Mattel banner, from American Girl to Fisher-Price, in broader ways that include movies, digital assets and more. He raised eyebrows in Hollywood in 2019 after hiring Greta Gerwig and Noah Baumbach—two directors and romantic partners known for adult-oriented features like “Lady Bird” and “Marriage Story,” respectively—to make a “Barbie” movie. Beyond the move to the big screen, Mr. Kreiz foresees a decade ahead of continued focus on the values and virtues underlying the toy shelf or online retailer.

After all, Barbie has kept up with the times, graduating from vacations in Malibu to the medical profession, astronomy and even president of the United States. What will Mattel’s future look like?