The developer of Arlington's $100 million Parkington Shopping Center renovation project yesterday announced that Forest City Rental Properties Corp., a Cleveland development firm, is its new partner in the retail portion of the shopping center venture.

Officials of May Centers Inc. also unveiled plans to expand the project from a one- to three-level complex of shops and restaurants and add 100,000 square feet of space for a third major department store. The proposed changes also provide for an urban park on a southeastern portion of the site, located along Wilson Boulevard between Glebe Road and North Randolph Street.

May Centers, which owns the 14-acre mall site to be renamed Ballston Common, said the company is still seeking developers to replace the Oliver T. Carr Co. of Washington. Carr recently withdrew plans to build a nine-story office building as part of the project.

May Centers vice president John D. Moore said the company has been working for the past few months with Forest City Rental to expand retail space in its redevelopment of the Parkington Center. The two firms are currently involved in a similar project in Charleston, W. Va.

The expansion plans, submitted to the Arlington County Board, amend previously approved plans. The new plans would require the demolition of parts of an existing parking deck to allow for a more prominent location of a third department store not yet identified.

County Board Chairman Ellen Bozman said that the new plans look like a "better design without a lot of change . . . ."

Project manager Richard Shields said the firm still plans to begin construction in January 1984 with the mall's opening set for the fall of 1985.