When Boeing named Stephanie Pope to the new position of chief operating officer in December, the move was widely viewed as a sign that she might succeed the company’s chief executive, Dave Calhoun, in the next few years.

Four months later, facing its second big crisis in five years, the company has begun a fresh search for another chief executive. And Ms. Pope appears to be just one of several potential candidates for one of the most prominent and perilous positions in corporate America: fixing Boeing.

Late last month, the company announced that Mr. Calhoun would step down at the end of the year, much earlier than expected. The chairman of Boeing’s board vacated his position immediately, and the head of its troubled commercial planes business departed.

The management changes came after a panel blew off a 737 Max 9 jet during an Alaska Airlines flight in January, an incident that renewed questions about the quality and safety of Boeing’s planes several years after two fatal crashes of 737 Max 8 planes in 2018 and 2019.

As recently as 2021, Boeing had signaled that Mr. Calhoun, who took the company’s reins after the Max 8 crashes, would not leave anytime soon. The company’s board raised the mandatory retirement age for the chief executive to 70, from 65, a change that would have allowed Mr. Calhoun to stay in the job until April 2028.

But the Alaska Airlines incident disrupted those plans, and Boeing’s board must now identify a new top executive on a more compressed timeline. That new leader has to be someone who can prove to regulators, airline executives, employees and investors that Boeing is firmly committed to improving the quality and safety of its products.