Nothing sets an agency on edge like a reorganization -- unless it is the boss leaving just as people are beginning to get accustomed to the proposed changes.

That's what has happened to the Office of the U.S. Trade Representative, where William E. Brock set some teeth on edge two months ago with a reorganization plan that would make the already lean office even leaner. Then President Reagan tapped Brock to be secretary of Labor, and the reorganization was put on hold.

Now the trade specialists are awaiting the arrival of Brock's successor, Clayton Yeutter (it rhymes with writer), who doesn't expect to be on board full time until June 1, as they cope with Japanese and European friction and preliminary planning for a new round of global trade talks.

Yeutter is no stranger to the office, having been a deputy special trade representative in the Ford administration, back in the days when the boss was called the special trade representative instead of the unspecial U.S. trade representative. But insiders wonder who in the upper echelon will go to the Labor Department with Brock, who will stay at the trade office and who will go off to other jobs.

Although there have been no public announcements, it is widely assumed that Dennis Whitfield, Brock's chief of staff, and David Demarest, his public affairs chief, will move with him to Labor. Both came with Brock from the Republican National Committee.

Yeutter, meanwhile, is keeping a low profile until his Senate confirmation hearings, which are expected to be next month. He reportedly has a stack of about 400 unreturned phone calls on his desk at the Chicago Merchantile Exchange, which he heads, and has turned down appearances on the network television interview shows.

He will be in Washington this weekend, however, because his daughter, Kim, is Nebraska's Cherry Blossom Princess in the festival.

In his one news conference, the day after Reagan announced his nomination, Yeutter, 53, placed himself squarely within the free trade ideology of this administration.

But he said, without being specific, that the United States might have to become tougher with its trading partners if they restrict trade in ways that hurt U.S. interests. "There has to be a level playing field out there. It's important that the United States protect its own interests on trade issues," the Associated Press quoted him as saying during the April 4 news conference in Chicago.

He declined to comment on the burning trade issue of the day, the worsening frictions with Japan, remarking that "it is not productive" to make trade policy in such an "emotional environment."

Yeutter, who is a Nebraska lawyer and rancher and served as an assistant secretary of Agriculture in the Nixon and Ford administrations, is likely to be a favorite of the farm bloc. He acknowledged that American farmers have suffered a "double whammy" of a strong dollar and high interest rates, which have hurt agricultural exports.

Agricultural trade is a major irritant with the European Community, whose heavily subsidized products are blamed for taking markets in other countries away from the American farmer. MORE TRADE REPS . . .

President Reagan has announced three new appointments to the Advisory Committee for Trade Negotiations.

Washington lawyer Stephen I. Danzansky will succeed James Dutt; Linda Wachner, a member of the board of directors of the Los Angeles Chamber of Commerce and a former president of Max Factor & Co., will succeed John G. Hutches; and Virginia S. Weinman, president of Symbiosis in Menlo Park, Calif., will succeed William Agee. Lloyd Hacker, president of the American Retail Federation in Washington, was reappointed.