WASHINGTON — The Heritage Foundation, the conservative think tank that has influenced Republican White Houses and shaped conservative policy since the 1970s, named a new president on Tuesday who has deep ties to the party’s social conservative and evangelical Christian wing as it moved to steady itself after a year of internal turmoil.

Kay Coles James, who served in the administrations of Ronald Reagan, George Bush and George W. Bush, will fill the vacancy left this year when Heritage’s board unexpectedly removed Jim DeMint, the former senator from South Carolina who became a leading practitioner of the uncompromising, no-apologies style of conservatism that characterized the Tea Party revolt.

If Mr. DeMint’s appointment in 2013 was a sign that Heritage was embracing the grass-roots energy that had proved so disruptive to the Republican Party, naming Ms. James was an acknowledgment that many inside the organization believe Heritage had strayed from its mission of acting as the intellectual and policy guide star for conservatives.

Like other institutions that had grown comfortable in their roles as fixtures of the political establishment, Heritage has struggled to find a meaningful role for itself in President Trump’s Washington. Some inside the group complained that it had little influence in shaping debates on Capitol Hill that conservatives should have been far better prepared for — like the struggle over repealing the Affordable Care Act.