President Biden’s decision to nominate Lael Brainard to become Federal Reserve vice chairwoman elevates a veteran policy maker and economist who has been a strong ally of Chairman Jerome Powell on the central bank’s boldest policy decisions during the pandemic.

Ms. Brainard was a key adviser to Mr. Powell as the Fed scaled up emergency-lending backstops last year, and she provided influential intellectual support for his effort last year to revamp the Fed’s policy-setting framework. Under the new framework, the Fed set aside...

President Biden’s decision to nominate Lael Brainard to become Federal Reserve vice chairwoman elevates a veteran policy maker and economist who has been a strong ally of Chairman Jerome Powell on the central bank’s boldest policy decisions during the pandemic.

Ms. Brainard was a key adviser to Mr. Powell as the Fed scaled up emergency-lending backstops last year, and she provided influential intellectual support for his effort last year to revamp the Fed’s policy-setting framework. Under the new framework, the Fed set aside its practice of raising rates to pre-empt inflationary pressures and pledged to keep interest rates low to foster a faster and broader labor-market recovery.

Ms. Brainard has been especially outspoken about avoiding the mistakes of raising interest rates prematurely after a downturn when interest rates are near zero.

Mr. Biden on Monday also said he would nominate Mr. Powell to a second term as Fed chairman. Now, both leaders face perhaps their trickiest policy challenge of the past four years: A bout of inflation that is proving to be more stubborn than anyone at the central bank anticipated is raising questions over how the Fed should set policy in the months ahead.

Mr. Powell and Ms. Brainard have underscored the importance of not raising rates until labor markets are tight to build up the credibility of their new framework this year. But with inflation running well above the Fed’s 2% target, they are facing questions over how long they can maintain that stance before eroding the central bank’s credibility.

Brisk demand for goods, disrupted supply chains, temporary shortages and a rebound in travel have pushed 12-month inflation to its highest readings in decades. Core inflation, which excludes volatile food and energy prices, rose 4.1% in October from a year earlier, according to the Fed’s preferred gauge.

Fed Chairman Jerome Powell has been steering Fed policy through a changing pandemic.

Photo: Andrew Harnik/Associated Press

“We’re entering a period of great policy uncertainty. Will they raise rates in the first half of 2022? Are they going to have the resolve to wait? It’s going to take a lot of courage,” said Derek Tang, an economist at LH Meyer Inc., an economic-forecasting firm.

“Brainard has been very focused on maintaining maximum employment,” said Mr. Tang. “If there’s a difference between how Powell and Brainard characterize that threshold, the market could ask, ‘Who should we listen to?’”

If confirmed by the Senate, Ms. Brainard would succeed Fed Vice Chairman Richard Clarida, whose term on the central bank’s board expires in January. The Fed’s vice chair, along with the New York Fed president, is part of the inner circle of advisers—known as the troika—that shape the agenda for monetary-policy deliberations by the Fed’s rate-setting committee.

When the coronavirus pandemic sparked a global dash for dollars that overwhelmed the ability of many markets to function in March 2020, Mr. Powell asked Ms. Brainard to join the group, an arrangement that has continued to the present.

Before joining the Fed in 2014, Ms. Brainard helped manage President Barack Obama’s response to the 2008 financial crisis during four years as the Treasury Department’s top financial diplomat, making her one of the few Democrats intimately involved in responding to the last two economic shocks.

Ms. Brainard served as an adviser to President Bill Clinton on international economics in the late 1990s. She also served as a staff economist on the White House Council of Economic Advisers in the George H.W. Bush administration.

Even though Mr. Powell and Ms. Brainard have been aligned on monetary policy, there are questions over how they will resolve differences on other issues. Since he became chairman in 2018, she has dissented on 23 board votes, often to protest against loosening banking rules imposed after the 2008 financial crisis.

Among the six sitting Fed governors, Ms. Brainard has spoken the most enthusiastically about the central bank adopting a digital dollar while raising warnings about the risks of unregulated private digital money, including so-called stablecoins that seek to tie the value of their respective offerings to the dollar.

Fed Vice Chairman Richard Clarida’s term expires in January.

Photo: Al Drago/Bloomberg News

Ms. Brainard also expressed concern over the dollar losing its dominance in international payments if other central banks, including in China, press ahead with their digital currencies.

Mr. Powell, on the other hand, told lawmakers this summer he was torn over whether the benefits of issuing a digital dollar outweighed the costs, including potentially disrupting the banking system.

Ms. Brainard has pulled the Fed her way on some key banking issues, including twice in 2019, both times with crucial backing from Mr. Powell. First, the Fed bucked opposition from big banks when it voted to establish a round-the-clock payment system for banks to exchange money, a proposal she spearheaded.

Later, the Fed opted against joining two other federal banking regulators, the Office of the Comptroller of the Currency and the Federal Deposit Insurance Corp., on a proposal to overhaul rules implementing the Community Reinvestment Act, a 1977 law designed to end racial lending disparities. After Mr. Biden’s election, the OCC scrapped its proposed overhaul.

Ms. Brainard “almost single-handedly saved the Community Reinvestment Act and managed to get four Republican governors to vote for her outline,” said Jesse Van Tol, chief executive of the National Community Reinvestment Coalition.

Financial-industry officials welcomed both of Mr. Biden’s Fed nominations. “We expect regulators will continue to hold the largest banks to the high regulatory and supervisory standards that have remained in place to support a resilient and essential part of the U.S. financial system,” said Kevin Fromer, chief executive officer of the Financial Services Forum, which represents the largest U.S. banks.

Ms. Brainard received 61 votes during her confirmation in 2014, including from four Republicans who are still in the Senate.

The daughter of an American diplomat, Ms. Brainard grew up on both sides of the Iron Curtain in Germany and Poland during the Cold War. She has credited that upbringing with fostering her interest in economics. “I was fascinated by how two countries so close in geography and resources could diverge so sharply simply by being separated by the Iron Curtain,” she said in a 2014 speech in Claremont, Calif.

Life in Poland was grim, with an economy that suffocated under a heavy state apparatus, she recalled in a 2017 interview with the college newspaper at Wesleyan University, where she completed her undergraduate degree. The most successful parts of the economy were farming and small-business enterprises that had “the least amount of red tape and the greatest role for individual initiative,” she said.

Ms. Brainard received her Ph.D. in economics from Harvard University after a stint working for consulting firm McKinsey & Co. She is married to Kurt Campbell, who is Mr. Biden’s point person on Asian affairs on the White House National Security Council.

Write to Nick Timiraos at nick.timiraos@wsj.com