GTE Business Communication Systems Inc., a new division of GTE Corporation, will set up headquarters at a 180,000-square-foot site in Reston.

Ground already has been broken for the new headquarters, which will consolidate administrative, marketing, research and development and manufacturing activities of the division from facilities located in Connecticut and Florida.

Initial occupancy of the new building, near Dulles Airport Access Highway and the proposed Fairfax Parkway, is set for next fall.

GTE Business Communication Systems Inc. is the telephone manufacturing arm of GTE Corp. The division makes telephones and develops, manufactures, sells, installs and maintains voice and data communications systems used primarily by private companies and government organizations.

Other developments in area commercial real estate include:

* Honeywell has announced the grand opening of its new Customer Training and Demonstration Center in Crystal City on August 17, 18 and 19. Current and new users of Honeywell's office systems and the general public are invited.

The Arlington Center, in Suite 609 of the Crystal City Gateway, 1235 Jefferson Davis Highway, is one in a series of office automation support centers the company is opening throughout the United States to augment its existing training and educational facilities.

Besides offering customer training, the Arlington center will serve as a demonstration and benchmark site for industry analysts and prospective customers.

The center includes conference and classroom space, a demonstration area, 12 work stations that connect to a Honeywell small computer system, letter-quality printers and a mass storage unit.

* Avis Car Leasing Arlington, Va., has been relocated to One Flint Hill, 10530 Rosehaven St., in Fairfax, Avis recently announced.

The station will serve the long-term leasing market for companies or organizations with fleets of from one to 1,000 vehicles.

* The Fort Washington Care Center, a new nursing home for Prince George's County, is now under construction at Indian Head Highway and Livingston Road in Fort Washington. The 150-bed facility, which will employ about 150 persons, is expected to open in June 1983.

Construction of the $3.5 million project, a three-story brick and masonry building, is under the direction of Gardiner & Gardiner Inc., general contractors located in Crofton, Md.

The 52,478-square-foot building will include six private and 144 semi-private comprehensive-care beds, in addition to nursing stations and common areas.

* Advanced Office Systems has leased 1,135 square feet at 7101 Wisconsin Ave. in Bethesda. The new company sells microcomputer systems encompassing hardware, software and consulting services, focusing on small- to medium-size businesses and professional markets.

* Sparta Inc., a systems engineering and analysis company, has opened a Washington office, leasing 796 square feet at 7926 Jones Branch Dr. in McLean. The 3-year-old company, with headquarters in Alabama, performs analysis of weapons systems for the federal government.

* Hill, Taylor and Company, a CPA firm based in Chicago, has opened a Washington office 1120 G St. N.W. by leasing 1,658 square feet. The firm handles accounting for state and local governments, nonprofit organizations, and small companies, as well as pension and retirement plans.

* Steelcase Inc. has signed a lease for 6,000 square feet of space in the new Washington Design Center and will open a showroom in the facility in early 1983, the company recently announced.

* Dupree Associates recently unveiled plans for Parkridge, a business park located on a 46-acre site in Reston, next to Dulles Airport Access Road.

Planned to be built in six phases, Parkridge Business Center will offer 11 buildings totaling 700,000 square feet of space. Phase 1, with 120,000 square feet of floor space, will be completed next year.