People are feeling stuck in their jobs. Bosses are starting to worry.

Many workers say they are considering that question as they feel stuck in their roles. With the white-collar labor market cooling and declining turnover leading to fewer internal moves, a sense of malaise and frustration is growing inside big companies.

At a range of companies, employers are trying new tactics to spur movement. Consulting giant McKinsey is increasing the size of its mobility budget to let employees take projects in new cities, if only for a few months, to help staffers grow. Credit-card issuer Synchrony Financial is letting some people apply for temporary positions on other teams. Exact Sciences, a diagnostics company, is expanding some roles to give people fresh challenges.

“The very best people want new experiences,” said Kevin Conroy, chief executive of Exact Sciences, which is based in Madison, Wis., and makes the colon-cancer test Cologuard. “They want a career path, and they want to be promoted.”

When lots of people are quitting, it is easier to move people around or to bring in outside hires to inject fresh energy to teams, executives say. The environment now is different.

Lower Turnover

Voluntary turnover within companies has fallen from 17% in 2022 to 12% so far this year, according to data from professional-services company Aon, which surveys employers on pay and attrition trends. What companies call “regrettable turnover”—losing employees they would rather keep—has also declined as more high performers stay put, according to the Aon data.

The U.S. unemployment rate has steadily climbed in recent months, rising to 4.1% in June. Hiring remains strong in many parts of the economy, though wage gains have eased and some employers have chosen to keep open positions unfilled. Rates of promotion into management have fallen across nearly all age groups, according to data from payroll-services provider ADP.

The challenge for companies, executives say, is how to find ways to create growth opportunities even if that doesn’t mean a substantial pay raise or a title change. In an era of efficiency, CEOs are often reluctant to add roles or create layers of additional middle managers within organizations. Instead, many companies are focusing more on training, pushing managers to give more coaching to employees in one-on-one meetings to propel staffers forward.

“There’s much greater emphasis around skills-based approaches: How do you create better pathways, more mobility, more development?” said Brooke Weddle, a senior partner at McKinsey who is a leader in the firm’s people and organizational performance group.

At Synchrony Financial, which has about 20,000 employees, the company has experimented with job swaps within a range of departments, including tech, credit and finance. An employee in one role can switch with a colleague elsewhere for as little as 90 days to a year or more.

“It helps with some of that lack of natural attrition,” said DJ Casto, Synchrony’s chief human resources officer. “You’re building a new skill set and experience.”

Job Swapping

Among those swapping roles is Matt Menning, an Atlanta-based associate vice president at Synchrony. In May, he left his position in operations for a three-month stint in engineering as an IT quality assurance lead, helping a team of engineers test software code and troubleshoot issues. Another employee temporarily swapped into his operations job, and Menning will return to his prior role in August.

A more-than-10-year company veteran, Menning had been in his position for almost two years and saw the job swap as a way to build new skills. “I’m at a point where I want to start looking at the next step, the next level within our company,” the 46-year-old said. “I’m learning every day.”

HR chief Casto has discovered that, in periods of lower turnover, some employees might not want a new position—but they don’t want to feel trapped in their current roles.

“They want the ability to think about doing something net new and being empowered to do what’s best for them,” he said. “When you’re just told there isn’t opportunity or options, then all of a sudden your mindset changes.”

McKinsey increased its mobility budget to allow people to take on projects in new cities, said Bob Sternfels, the consulting firm’s global managing partner. The goal, he said, is to make it easier for people to gain new experiences elsewhere, sharpening their skills and giving them a more global understanding of the world.

“If you’ve worked in two or three countries, you have a very different perspective than if you’ve only worked in one,” he said.

A job market like this one favors employers. Even so, it is a mistake for companies to ignore workers’ feelings or ambitions, veteran human-resources executives say, because talented employees retain options.

“We’ve all seen the market come and go, and when it comes back, they’ll all quit,” said Bob Toohey, chief human resources officer at the insurer Allstate.

Internal Recruiting

As Allstate’s hiring slowed, Toohey asked the company’s recruiters to focus their efforts internally. Recruiters are now setting up 20-minute to hourlong coffee chats with employees across the company, asking them what they would like to do in the future and how they are thinking about their careers. Initially, some employees blanched at those calls, wondering what HR wanted.

“When you get a call from a recruiter internally, you start to go, ‘Am I losing my job?’” Toohey said.

Instead, the conversations have had the effect of showing employees that the company is interested in their careers. When jobs come open, Allstate has given priority to filling them with existing staff. The company this year has filled 60% of its roles internally, up from 45% last year.

“That’s creating this internal movement,” Toohey said. “We’re using our recruiters as talent agents.”

Allstate is also rolling out an internal tool this month to make it easier for employees to see open projects on other teams. Managers don’t need to approve an employee taking on a new role, a restriction that can hold people back from pursuing new experiences and that was removed in 2022.

“We want people to think about their career both moving left, right and up,” Toohey said. “I think we have to get away from just: ‘I move up.’ It’s ‘How do I progress?’”

Write to Chip Cutter at chip.cutter@wsj.com