International Business Machines Corp., the second-largest private employer in metropolitan Washington, is adding more office space to its Gaithersburg complex, a spokesman for the national computer manufacturer said last week.

Construction has begun on a three-story, 430,000-square-foot building next to the existing IBM Federal System Division and National Accounts Division facilities in Gaithersburg, the spokesman said. The 121-acre complex is located at 18100 Frederick Pike, north of the Montgomery Village Avenue exit on I-270. The expansion is expected to be completed in the spring of 1987.

The new building will be used for the National Accounts Division, helping to consolidate employes from other Gaithersburg locations in the main complex. IBM employs 14,500 people in the metropolitan Washington area, 3,800 of whom work in Gaithersburg. The new building will provide additional offices, conference and presentation rooms, cafeteria and computer facility.

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

*The Agency for International Development has renewed its original lease plus additional space for a total of more than 106,000 square feet at 1800 North Kent St. in Arlington. The multi-year lease has an aggregate value of more than $9.5 million.

*Dallas-based Lincoln Property Co. has begun construction on Lincoln Place, a 514,000-square-foot office complex on Army Navy Drive between South Fern and Haynes streets. The 12-story twin towers will be available for lease by Lincoln Propery in the spring of 1987.

*Metier Management Systems Inc., a subsidiary of Lockheed Corp., signed a five-year, $1.7 million lease for 16,711 square feet at the Mark Center Office Park at 4900 Seminary Rd. in Alexandria.