May 11 (Reuters) - Kevin Warsh, U.S. President Donald Trump's pick to be the next chair of the Federal Reserve, on Monday cleared a key procedural hurdle in the Senate, moving him closer to Senate confirmation and a smooth handoff from Fed Chair Jerome Powell, whose leadership term ends on Friday.

Here are some details and context:

-- The Senate is expected to follow Monday's so-called cloture vote with a vote to confirm Warsh for a 14-year term as Fed governor as soon as Tuesday. Lawmakers would then start the confirmation process for a concurrent four-year term as Fed chair, with a vote on that nomination to come as soon as Wednesday.

-- The Republican-controlled Senate is expected to approve Warsh to be the Fed's next leader at a time when the central bank's independence is being tested.

-- Trump's unprecedented measures to exert control over the Fed include his attempt to fire Fed Governor Lisa Cook in a case that is now before the Supreme Court, and his support for a Department of Justice investigation into Powell's management of a building renovation. A federal judge ruled the probe was pretext for pressuring Powell to cut rates or resign.

-- The DOJ dropped its investigation, but its lead prosecutor in Washington says she could reopen it, and Powell says he will stay on at the Fed until it is truly over.

-- Powell says he is concerned "about the series of legal attacks on the Fed which threaten our ability to conduct monetary policy without considering political factors." Warsh has not weighed in on the Trump administration's actions.

-- Warsh says he plans "regime change" at the Fed, including tightening its coordination with the Treasury and the administration on non-monetary policies, and setting it on course for a smaller balance sheet.

-- Trump says he expects Warsh to cut rates. Warsh has said he has not made any promises to Trump on monetary policy.

-- The Fed chair has one of 12 votes on interest-rate decisions, and one of 19 voices at the policy-setting table.

-- At their meeting last month, Fed policymakers voted to keep the policy rate in the 3.50%-3.75% range, and three central bankers dissented to express their openness to a possible interest-rate hike.

-- The Fed's next meeting, and its first under a possible Chair Warsh, is scheduled for June 16-17.