As Wall Street grapples with the election of Donald Trump as the next US president, it appears the order of the day is uncertainty.

Among the myriad uncertain consequences of Trump’s election is the real possibility of a major shake-up at the Federal Reserve.

Jefferies economist Sean Darby said that in terms of possible problems for the economy going forward the “main risk is monetary policy uncertainty.”

The most striking uncertainty for some analysts is the political independence of the Fed – to not have monetary-policy decisions influenced by ever-shifting political tides has long been a key aspect of the central bank.

Some analysts now say that independence may no longer be assured.

"Ultimately," T. Rowe Price's chief US economist, Alan Levenson, said in a note to clients Tuesday night, Trump's proposals "threaten to undermine global faith in the independence of the Federal Reserve and the geopolitical standing of the United States."

Additionally, some analysts have questioned whether Fed Chair Janet Yellen will remain in her job under the new administration given Trump's pointed criticism of the central bank's policies and her leadership.

"The future of Janet Yellen's chairmanship and the accommodative nature of Fed monetary policy are in doubt," Edward Mills of FBR Capital Markets said.

Deutsche Bank strategist George Saravelos agreed that the future of Yellen's job was uncertain.

"Even more importantly the market will be looking for confirmation that Chair Yellen will not resign," Saravelos said in a note to clients. "Trump has been particularly critical of her term so policy continuity will be particularly important."

On the other hand, Michael Feroli, an economist at JPMorgan, wrote before the election that Yellen's resignation was unlikely. For one thing, Feroli noted, that there is seemingly no way that Trump could actually fire Yellen.

The economist also said a Federal Reserve chair resigning was unprecedented, but there is another political reason for Yellen to stay on. "Moreover, we don't see a rationale for the apparently Democratic Yellen to give President Trump even more influence over the course of monetary and regulatory policy by immediately stepping down," Feroli wrote. "That said, we doubt she would stay on as Governor even after her term as Chair expires."

In the near term, analysts are also split on whether the Fed will interest raise rates in December. Market probabilities for a rate hike in December have fallen from 84% on Tuesday to as low as 42% overnight, according to Bloomberg data.

On the one hand, the market volatility following the election has convinced some that the Fed will be on hold.

Quentin Fitzsimmons, an international bond manager at T. Rowe Price, said market uncertainty coming out of the election would cause the Fed and other central banks to wait for more clarity before adjusting policy.

"When faced with volatility central banks tend to kick the ball further into the long grass - so they may end and maybe deepen their easing cycles," Fitzsimmons said.

Saravelos agreed that a December rate hike was dead.

"When it comes to monetary policy, in the short term, it looks like a December rate hike is off the table," the strategist said.

David Kelly, the chief global strategist at JPMorgan Funds, said Trump's election at least lowered the chances of a hike. "The uncertainty and volatility following the U.S. election will, for now, reduce the probability of a Federal Reserve rate hike in December," Kelly wrote, "although the Fed will want to leave its options open until it can assess the market and economic fallout from the election result."

On the other hand, others said the strong fundamentals of the economist would keep the Fed on track.

"Unless market volatility weighs on the real economy, particularly jobs, we think the Fed still hikes in December," David Bianco, the chief US equity strategist at Deutsche Bank, said in a note to clients.