“We are seeing headwinds. It’s a different type of busy than we were,” said Jodi Schwimmer, who co-leads Reed Smith LLP’s financial industry group.

Overall law firm demand, measured in billable hours logged, dropped 0.8% in the first nine months of 2022, compared with the same time frame last year, according to a report released in mid-November by the Wells Fargo Legal Specialty Group. Revenue has grown 4.6% in 2022, compared with 14.4% in the same period in 2021. Expenses have grown 12.8% in 2022, compared with the previous year, squeezing profit margins for firms, according to the report.

“Firms did hire in anticipation of demand. It’s come up a bit short,” said Owen Burman, senior consultant with Wells Fargo.

Mr. Burman said weakening demand isn’t even across the board and in certain regions, including Texas and Florida, law-firm practices are thriving even as work flattens in bigger markets, such as California and New York.

According to data provided to The Wall Street Journal by Leopard Solutions, which tracks and analyzes hiring in the legal industry, large firms are responding to the slowdown by cutting back on the hiring of associates from other firms, though demand at the partner level remains strong.

“We see the big law firms reverting back to prepandemic normalcy,” said Phil Flora, a vice president at Leopard Solutions. “Jobs are closing, and they aren’t refilling positions if people leave.”

In some cases, law firms are using the performance-review process to weed out underused associates hired during the boom of recent years, law-firm insiders and consultants said.

The top 100 grossing law firms saw a 13% reduction in the number of lateral associate hires from Jan. 1 to Nov. 15, according to the Leopard data. In that same time frame, lateral partner hires increased 17%, the data show.

Brad Karp, chairman of Paul, Weiss, Rifkind, Wharton & Garrison LLP, said despite potentially tough times ahead, firms are still willing to pay top-dollar for high-performing partners in strategically important practice areas.

“Today’s legal market is marked by aggressive poaching by competitors, with especially intense demand for star partners,” Mr. Karp said. “This puts increased pressure on elite law firms to bind their partners, through cultural glue and, if necessary, market-based compensation.”

Yvette Ostolaza, chair of Sidley Austin LLP’s management committee, said law firms will likely be cognizant of lessons learned from the 2007-2008 financial crisis, where firms made job cuts and froze hiring, only to be left without a pipeline of attorneys when the economy improved.

Several firm leaders said the economic downturn will mean companies need help with restructuring dwindling businesses or handling bankruptcy work, a boost for practices that specialize in these areas. They predict attorneys will shift work to these areas, instead of mergers and acquisitions that dominated 2021.

“Without question, what you are seeing now—and anytime you head into economic headwinds—is countercyclical practices picking up,” said Frank Ryan, DLA Piper’s global co-chair.

Government work also continues to boost some firms, as companies look to navigate complicated regulatory environments during the Biden administration.

Cravath, Swaine & Moore LLP, for example, announced plans this year to open a Washington, D.C. office that will have about 25 to 30 lawyers, including many former government officials.

Even with recent economic pressures, the outlook for the legal market remains healthy, despite the dip in demand after the recent boom, said Michael Ellenhorn, founder and chief executive at Decipher Investigative Intelligence, which studies law-firm hiring.

“Top line: Demand growth is slowing, but it has not fallen off a cliff,” Mr. Ellenhorn said.

Write to Erin Mulvaney at erin.mulvaney@wsj.com