Four weeks before President Trump signed an executive order seeking to restrict mail voting, he filed four nominations for vacancies on the Board of Governors of the U.S. Postal Service. All four were Republicans. Three have expressed doubts about who won the 2020 presidential election and the security of voting.

The selections broke with a longstanding practice of nominating board members in bipartisan pairs. Two of those nominees are on a fast track for approval, and could reach a full Senate vote when the chamber returns from recess in September. If confirmed, their appointments would effectively tip the board to a majority that is loyal to Mr. Trump.

The quiet attempt to restructure the leadership of the Postal Service comes as the president and his allies are trying to transform the 251-year-old agency into a central player in their quest to overhaul the nation’s elections. Last year, Mr. Trump took an unusually active role directing the board of governors to select the current postmaster general, David Steiner. And the president has imposed a highly partisan agenda on a historically apolitical institution: restricting mail voting, a practice more heavily used by Democrats than Republicans, which Mr. Trump has publicly acknowledged would benefit his party.

Control of the Postal Service grew even more critical on Monday, after the Supreme Court ruled to allow the administration to move forward with plans to restrict mail-in voting before the midterm elections. The justices cautioned that the decision was preliminary and should not be construed as a final determination on the legality of the order. It also remains unclear whether the administration can implement the restrictions in time for mail voting this year.

Senator Elissa Slotkin, a Democrat who serves on the Senate Homeland Committee with oversight of the agency, said the president is looking for people who will do exactly what he says and will carry out his order without respect for the U.S. Postal Service. Jonathan Smith, the head of the American Workers Postal Union, said postal workers are worried about being ordered to implement policies that are legally questionable. Since he returned to power last year, Mr. Trump has recruited allies for key roles across his administration who are willing to act on his false claims that his defeat in 2020 was rigged and the country’s election systems are not secure.

He has pressed for criminal investigations of election officials in states he lost in 2020. His top legislative priority is enacting a law that would require proof of citizenship to register to vote. He has deployed the Department of Homeland Security to scour state voter rolls for noncitizens.

Few agencies are as central to this mission as the Postal Service. And few are as blatantly straining the boundaries of executive power. The Constitution grants the president no authority over elections, an area of governance that only Congress and the states may regulate.

Yet Mr. Trump has instructed the Postal Service to effectively police mail voting and decide which ballots can be delivered. He has urgently stayed on the issue in the midst of a daunting midterm cycle for Republicans, stating publicly that his party could keep control of Congress if mail voting could be blocked. In March, he signed an executive order that would grant the Posta...