Thanks to rapid suburban growth, some Northern Virginia will gain additional representatives in the Virginia legislature when it is redistricted after the 1980 census, a state report released today predicted.

The report said the gains will come at the expense of older communities-such as Arlington and Alexandria-which have experienced population losses or slow growth in recent years.

The report said Fairfax County, whose population has grown more than 20 percent since 1970, will get at least one more House of Delegates seat, and may share a second new delegate with Fairfax City and Falls Church. The county currently has 10 delegates, including five who represent the northern half of the county along with Fairfax City and Falls Church.

Loudoun and Prince William counties, which now share three delegates with Manassas and Manassas Park, will pick up one and perhaps two more delegates, according to the report by the state Division of Legislative Services.

Fairfax may also gain one state senator. The county currently has five senators, two of whom are shared with other localities.

The Northern Virginia gains will come at the expense of older cities, where population is decreasing, the report said. It projects that Alexandria and Arlington may lose the "floater" House of Delegates seat that they presently share. Richmond and Norfolk are other citites likely to lose some representation, the report said.

The report also predicted less dramatic changes in the states's 10 congressional districts, but said the 8th Prince William, and parts of Fairfax and Stafford counties, should be reapportioned to reflect its growing population. The district's population has increased more than 25 percent in the last 10 years.

There is also a chance Virginia will qualify for an 11th congressional seat, if the state population grows slightly faster than projected or national growth is less, the report said.

If the state gets another seat, the report said, "the present boundary lines would have to be erased and districting started virtually from scratch." Because Northern Virginia is the state's most rapidly growing area, it would undoubtedly at least share an additional seat, the report said.

The report was prepared by division researcher Richard W. Hall-Sizemore for Del. Ford Quillien, a Southwest Virginia Democrat. Its findings are based on 1980 population projections made two years ago by the state Department of Planning.

The Virginia constitution requires the General Assembly to redistrict the state in 1981, based on 1980 U.S. Census figures.

The planning department projects a total 1980 state population of 5.3 million. The report says that under the Supreme Court's "one man, one vote" mandate, each of the state's 100 delegates should represent 53,000 people, or 1 percent of total population. Each of the 40 state senators, should represent 132,000 people or 2.5 percent, and each congressman 53,000 or 10 percent. In large urban population centers such as Northern Virginia, district lines often cross a number of local boundaries