Paul B. Simmons, special assistant to the president and former deputy commissioner of Social Security, is leaving the government July 15 to become president of the Health Industry Distributors Association. The trade group bills itself as the largest association of firms supplying the health-care industry. Before joining the Social Security Administration in 1981, Simmons had worked as a journalist and as a senior aide and executive assistant to Illinois Gov. James R. Thompson (R), as associate commissioner of social services of New York State and as executive assistant to the New York state commissioner of health.

As expected, President Reagan has nominated Michael Baroody, deputy assistant to the president and director of public affairs, to be assistant secretary of Labor for policy. Baroody served as an executive assistant to Labor Secretary William E. Brock when Brock was U.S. trade representative. Baroody would replace John F. Cogan.

At the Health and Human Services Department, rumors persist that Carolyne K. Davis, head of the Medicare and Medicaid programs, will resign by early fall, probably to assume the presidency of a college. If so, at least some top department officials would like to offer her job to Sheila Burke, longtime health policy aide to Senate Majority Leader Robert J. Dole (R-Kan.).

Department sources, meanwhile, said it appears that the White House has finally cleared Food and Drug Administration chief Frank E. Young for elevation to assistant secretary of HHS for health, and Ron Robertson, former counsel of the Reagan-Bush campaign committee, for the job of HHS general counsel. The White House clearance was first disclosed by the trade journal, Medicine and Health.

The National Mediation Board, the agency responsible for solving collective bargaining problems at airlines and railroads, has only two members, and they are responsible, among other things, for electing a board chairman every year.

Member Walter C. Wallace, who recently worked on the tentative agreement between the nation's major railroads and the United Transportation Union, was "elected" to replace member Helen M. Witt, who worked on the recent contract settlement between United Airlines and the Air Line Pilots Association. Witt will remain on the board. A third position is vacant.