Coakley & Williams has announced the completion of all site preparation work for several future buildings at the Maryland Trade Center Park. The 34-acre site is located in Greenbelt on the Capital Beltway at the Baltimore Washington Parkway.

Already on the site is the Maryland Trade Center I, which was completed in 1981. The 16-story, 192,000-square-foot building is one of the tallest commercial buildings in Prince George's County. Among the tenants of the fully leased building are IBM, Lockheed and Bradford Communications.

A second office building of the same size is scheduled for opening in January 1984. A third is expected to open sometime later, depending on market demands.

Also planned for the park is a full service hotel and a 2,000-seat banquet and conference center. The hotel, to be owned by Coakley & Williams, will feature 212 guestrooms, a restaurant and lounge and is scheduled to open in September 1983. The facility will be operated by Martin's West, a caterer based in the Baltimore area.

Coakley & Williams owns and manages more than 1.5 million square feet of hotel and commercial property in the Washington area, including the Ramada Inn in Lanham, Md., and the Springfield Hilton in Springfield, Va.

Other recent developments in commercial leasing in the Washington metropolitan area:

* The first of two 75,000-square-foot, three-story office buildings has been completed at Linpro Park in Reston. Linpro Park is a joint venture between the Linpro Co., a national development firm with local offices in Germantown, and the Philadelphia Investment Corp., a subsidiary of CIGNA, the insurance company which resulted from the merger of Connecticut General Life Insurance Co. and the Insurance Company of North America. Leasing and management will be handled by Linpro.

* Western Development Corp. says construction has begun on an 11-story contemporary office building at 1444 I St. NW, between 13th and 14th streets, adjacent to the McPherson Square Metro Station. The building contains 74,135 square feet of space with one level of underground parking.

The contractor is Volpe Construction Co. and the projected completion date is November 1983. Financing was provided by Chase Manhattan Bank of New York.