Harper said she just wants to stay on SAG's board. She ran against the former "Little House on the Prairie" star and lost in both 2001 and 2002.
The guild's nominating committee tapped Gilbert last week.
Harper surfaced as a possible candidate following her effort to block the proposed merger between SAG and the American Federation of Television and Radio Artists, which last week fell 2 percent short of the required 60 percent approval the deal needed.
Other possible challengers include Kent McCord, Elliott Gould and Frances Fisher.