CALL it perestroika, union-style. America's largest private-sector union, the International Brotherhood of Teamsters, has just elected a reformer as president who promises to clean house. That's good news for the battered labor movement.For decades the Teamsters have been an embarrassment to labor. Their leaders were autocratic, linked to organized crime, and accused in later years of making sweetheart deals with employers. Three of the union's last five presidents spent time in jail. A fourth, Jackie Presser, was under indictment when he died. In short, the Teamsters' leadership resembled the autocratic and self-serving regimes of the former communist bloc. The turnaround began in 1988 when the federal government initiated an anti-racketeering suit. In order to settle that suit, the union allowed a court-appointed panel to oversee the union's management, remove corrupt leaders, and run a democratic election for union president. The process led to the Teamsters' first-ever popular election for president by secret ballot. The improbable winner is Ron Carey, a reform candidate who heads a Teamsters local in New York City. Mr. Carey campaigned for two years, pledging to clean up and revitalize the union. If he succeeds, the Teamsters could become America's most powerful union. Its 1.5 million members are concentrated in the strategic trucking and air-delivery industries. It wields political clout through a well-funded political-action committee. Carey faces several challenges. The union's sprawling and decentralized organization doesn't lend itself to a quick cleanup. Meanwhile, Teamsters for a Democratic Union, a sometimes militant reform group that backed Carey, will be looking for a tougher stance at the bargaining table. The problem is that trucking firms themselves are fighting off intense challenges from nonunion competitors. However, the immediate benefit of Carey's election is clear. He is poised to clean up a very dingy room in the house of labor. As Eastern Europeans and Russians now know, you have to clean house before new guests come inside.