When it comes to his economic agenda, President Biden faces a crucial decision on whom he’ll pick to lead the Federal Reserve. But Biden has another major choice about the Fed’s leadership, one that seems to have slipped almost entirely from public discussion.

The position — officially known as the Fed’s vice chair for supervision — may sound wonky beyond regulatory circles. It’s essentially the Fed’s top banking cop and has enormous implications for Wall Street oversight. The post opens mid-October when former president Donald Trump’s pick, Randal Quarles, finishes his term.

Some economists, along with people close to the Fed and the Hill, worry that the Biden administration has overlooked the post, undermining Democrats’ pledge to restrengthen oversight laws for the financial system that were relaxed during the Trump era.

“As 2008 revealed all too vividly, when banks get into trouble, the real economy and ordinary Americans suffer,” said Kathryn Judge, an expert on financial markets and regulation at Columbia Law School.

Judge, whose name has come up as a potential candidate, added that nominating someone “who really understands banks and banking, and who recognizes how much more could be done to promote the health of the financial system, could be critical to the long-term health of the economy.”

At the same time, there’s no clear consensus about who would be right for the job. The role requires extensive knowledge of the banking system. Some on the left would prefer a candidate who already has government or regulatory experience. There’s also a strong desire among Democrats for a nominee who would focus on how climate change affects financial stability.

The White House did not respond to specific questions about the vice chair for supervision role, possible nominees or the selection process. Referring to a range of Fed positions, White House spokeswoman Emilie Simons said Biden “will appoint the candidates who he thinks will be the most effective in implementing monetary policy.”

Many Democrats are focusing on the vice chair for supervision role because they hope to undo many of the policies Quarles put in place. Based on how long it can take for the Senate to confirm nominees, it’s unclear whether Quarles’s replacement would be in line before his term expires in October.

A former bank lawyer, Quarles has led the charge on easing restrictions on the banking system put in place after the Great Recession. His view, in part, is that banking regulations ushered in after the Great Recession could benefit from gradual refining and fine-tuning. Big banks have embraced those moves.

But his critics say that, put together, the cumulation of his policies cozied up to large firms and have made the financial system more vulnerable. During a Senate hearing in May, Sen. Elizabeth Warren (D-Mass.) told Quarles that “our financial system will be safer when you’re gone.”

Left-leaning economists, lawmakers and aides are particularly concerned about who becomes vice chair for supervision if Biden reappoints Jerome H. Powell to another term as Fed chair.

Powell — a Republican made chair by Trump — has garnered praise across Washington for his handling of the covid crisis. He has also won over many Democrats for his emphasis on full employment and the benefits of a tight labor market, especially when it comes to helping people of color get into jobs.

But Powell has sided with Quarles on banking policy, which is why some progressives don’t want Biden to reappoint Powell. Many are instead pushing for Lael Brainard, the lone Democrat on the Fed board. In addition to her views on monetary policy, Brainard has been a powerful voice against deregulation, consistently dissenting on policies that relax rules on the banking system.

If Powell gets another term as chair, Democrats and economists say Brainard would be a clear candidate for vice chair for supervision, given her strong views on Wall Street oversight. But those same advocates wonder if Brainard would prefer the role of vice chair — the No. 2 leadership position at the Fed — or if she would wait for a more sizable promotion, perhaps as a future treasury secretary or Fed chair, although they cautioned that they weren’t directly familiar with Brainard’s thinking. Brainard declined to comment.

Apart from Brainard, economists and others close to the Fed struggle to put other names forward. One name that comes up is Michael Hsu, the acting comptroller of the currency. Other Fed watchers suggest Sarah Bloom Raskin, a former deputy secretary of the Treasury Department and Fed governor, and Eric Rosengren, the president of the Federal Reserve Bank of Boston.

In the world of academia, some Democrats say they would support Judge, of Columbia Law School, or Jeremy Kress, an expert on bank regulation at the University of Michigan and a former Fed lawyer. It’s also possible that a candidate with less public name recognition — but plenty of in-the-weeds experience — could come from within the Fed system itself.

In the coming months, Biden will have multiple opportunities to shape the Fed’s makeup. There is already one vacant seat on the Fed board. Quarles’s term as vice chair for supervision expires in mid-October. In January, another vacancy opens that would allow Biden to install a new vice chair. Powell’s term expires in February.

Despite the staggered timeline, people close to the Hill and administration expect Biden will announce a package of Fed nominees at once. One idea is to assuage as many parts of the Democratic Party as possible, especially if Powell is reappointed. That announcement could come sometime in the coming weeks or October.

Still, some on the left say a package deal — one that pairs a Republican Fed chair with a slate of other Democratic nominations — wouldn’t reassure them of much.

“You cannot counterbalance the strong deregulatory views of Fed Chair Powell, who controls the Fed’s agenda, priorities and staff, with a vice chair for supervision who has a directly conflicting agenda that would repudiate three years of Powell’s votes and congressional testimony,” said Dennis Kelleher, chief executive of Better Markets, which advocates stronger market regulation. “That would invite an unprecedented and very damaging civil war at the Fed.”

Some of the confusion around Quarles’s seat also depends on Quarles himself.

Even though his term as vice chair for supervision ends in mid-October, he can still finish out his time as a Fed governor for more than a decade. It’s unclear exactly how long he will stay.

“My term as a governor of the Fed, as you know, extends until 2032,” Quarles told Politico in June. “There’s a tradition in our family that people serve out their full terms on the Federal Reserve Board of governors, even if they are no longer the chair or the vice chair still.” (Quarles is related by marriage to former Fed chair Marriner Eccles, who stepped down as chair in 1948 and stayed on the Fed board until 1951.)

Some economists also say that if Quarles stays on as a Fed governor, he could manage to keep his influence as a major banking official until his replacement is confirmed.

Gregg Gelzinis, associate director for economic policy at the Center for American Progress, a center-left think tank, said the administration’s nominee should also “meet the moment” when it comes to emerging financial and systemic risks. That includes climate change policy, regulation of cryptocurrency and stable coins, along with competition policy.

“The stakes are extremely high,” Gelzinis said. “There are a lot of priorities that a vice chair for supervision and other new members of the Fed board are going to need to tackle when it comes to financial regulation and undoing the myriad of Trump’s harms. … Just getting back to the 2016 status quo is not the goal. That’s a good start.”