THE PERCEIVED HEIR APPARENT to House Speaker Robert DeLeo said on Thursday that he is stepping down to take a top job at the high-powered lobbying firm ML Strategies, a move that suggests the speaker is not inclined to retire anytime soon.

Rep. Brian Dempsey of Haverhill, the chairman of the House Ways and Means Committee since 2011, is leaving to take the job of senior vice president and chief operating officer at ML Strategies, a subsidiary of the law firm Mintz Levin Cohn Ferris Glovsky and Popeo. Dempsey’s office said he would not be available for comment.

Dempsey’s decision to leave the House indicates he was tired of waiting around for DeLeo to retire so he could move up. Several sources said they believe DeLeo, who pushed through the elimination of an eight-year term limit on the speaker’s position in January 2015, is likely to remain at the chamber’s helm for another three to four years. “Brian just wasn’t willing to wait around that long,” said one source.

The House is run in a top-down fashion by DeLeo, who himself moved up from the Ways and Means job to the speaker’s position in 2009. Dempsey meshed well with DeLeo; both lean conservative for Democrats and generally oppose new taxes. Dempsey entered the House in 1991, the same year as DeLeo, and the two officials are close friends who enjoy broad support within the body.

With Dempsey gone, DeLeo will now have to choose a Ways and Means chair who undoubtedly will be perceived by many as the person with the best shot of winning the speaker’s job once DeLeo retires. Others said the Ways and Means post is not a guaranteed stepping stone to the speaker’s job. The Ways and Means post is a big one, however, and the selection process could stir some turmoil in the House, as factions within the Democratic Party push for someone in line with their views.

“I think everyone assumed Brian was the next speaker. With Brian moving on, the speaker’s fight begins immediately,” said Rep. Russell Holmes of Boston. “Rest assured there will be a lot of people jockeying now and trying to galvanize support to be the next speaker, which I think is healthy for the building.”

Holmes said liberal-leaning groups in the House, including the Black and Latino Caucus, the Progressive Caucus, and the Women’s Caucus, will seek a greater voice in setting the House’s direction. “Our voices need to be louder in all pieces of legislation and in the budget,” Holmes said. “I look forward to a strong, robust discussion about not just who will be the next speaker, but the entire leadership team.”

DeLeo could not be reached for comment, but he issued a statement saying Dempsey was one of the best, if not the best, chairs of Ways and Means ever. He said Dempsey would be “an incredible asset” to Mintz Levin. “The process for selection of a new chair has begun, and we will have an announcement at the appropriate time,” he added.

One source said the list of possible replacements at Ways and Means isn’t that long. According to the source, the list includes, in no particular order, Rep. Stephen Kulik of Worthington, the vice chair of the House Ways and Means Committee; Rep. Jeffrey Sanchez of Boston, the House chairman of the Health Care Financing Committee; Rep. Joseph Wagner of Chicopee, the House chair of the Committee on Economic Development and Emerging Technologies; Rep. Tom Golden of Lowell, the House chair of the Telecommunications, Energy, and Utilities Committee; and Rep. Aaron Michlewitz of Boston, the House chair of the Financial Services Committee. Another source said he thought Wagner was an obvious choice, but suggested Rep. Jennifer Benson of Lunenburg, the House chair of the Consumer Affairs and Professional Licensure Committee, had a shot.

At ML Strategies, Dempsey, 49, will be filling the post vacated by William “Mo” Cowan, who left the firm in February to join General Electric. Dempsey plans to start at ML Strategies in September and spend his first year (when he is barred from lobbying on Beacon Hill) learning about the firm, including its Washington operations.

ML Strategies has become a powerhouse on Beacon Hill over the last several years. Its roster of lobbyists includes former governor William Weld, former state senator Steven Baddour, and a host of former government officials. The firm raked in more than $4 million in lobbying fees last year from a long client list that includes the Boston Symphony Orchestra, Boston University, Wynn Resorts, General Electric, Spectra Energy, the New England Aquarium, and Nalcor Energy.

In his new role, Dempsey is likely to be perceived as the heir apparent to Stephen Tocco, the chairman and CEO of ML Strategies. Tocco, a former cabinet official under Weld and a former chairman of the Massachusetts Port Authority, said Dempsey will be a great addition to the firm.

“He’s more than capable,” Tocco said. “We look forward to him being with us a long time in an expanded role as we go forward.”