The stunning upset election of Donald Trump on Tuesday has set off a behind-the-scenes political battle inside the Trump transition team in Washington. The battle is pitting conservative advisers against moderate Republicans. Both sides are working to take control of the incoming administration by arranging key appointments. According to sources close to the transition team working in offices at 1717 Pennsylvania Ave., key aides to New Jersey Gov. Chris Christie are seeking to have Mr. Trump arrange the appointments of moderate Republicans, possibly including some of the more than 100 who signed a letter during the campaign vowing never to work for the New York businessman if he was elected president. Some of the former officials who opposed Mr. Trump are now recanting that involvement in the letter in hopes of getting a job in the new administration. Mr. Trump has vowed that the Republican establishmentarians who opposed him will not get jobs in his administration. The word from two sources outside the transition team but familiar with discussions is that Mr. Christie may be replaced as the leader of the transition by someone more in line with Mr. Trump’s announced populist policies. The governor is under fire after convictions of two former aides in the traffic scandal dubbed Bridgegate. The key player in the conservative camp is Sen. Jeff Sessions, Alabama Republican and member of the Senate Armed Services Committee, who is in line to become secretary of defense. Others mentioned for the defense secretary position are former CIA Director R. James Woolsey and moderate Stephen Hadley, who was a national security adviser in the George W. Bush administration. Tidal McCoy, former Air Force secretary in the Reagan administration, is another defense secretary candidate. The moderates within the Trump camp include Mr. Christie and Sen. Bob Corker, Tennessee Republican and chairman of the Senate Foreign Relations Committee. Mr. Corker is lobbying hard for the plum post of secretary of state, while conservatives are pressing Mr. Trump to name John R. Bolton, former U.S. ambassador to the United Nations, to the seventh-floor power center at Foggy Bottom. Former House Speaker Newt Gingrich, who led the conservative revolution in Congress during the 1990s, also is hoping for secretary of state or another senior position. Former New York Mayor Rudolph W. Giuliani has been mentioned as attorney general or homeland security secretary. David Clarke, the sheriff of Milwaukee County, Wisconsin, also has been mentioned for the Homeland Security Department post. Another Trump adviser likely to be named to a senior post is retired Army Lt. Gen. Michael Flynn, who could be named White House national security adviser or director of national intelligence.