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.

Some economists say 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. 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.

Even more importantly the market will be looking for confirmation that Chair Yellen will not resign. Donald Trump has been particularly critical of her term so policy continuity will be particularly important.

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. The market uncertainty coming out of the election would cause the Fed and other central banks to wait for more clarity before adjusting policy.

Some economists believe that 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, 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.