Penned by William Blake Herron, the pilot is being produced for TNT by Beacon Pictures, with Armyan Bernstein serving as executive producer.
Best known for her work in "Basic Instinct" and "Casino," Stone will play America's first female vice president, Natalie Maccabee, "a woman with brains, beauty, and a cool composure that belies a restless mind," the cable network said in a news release.
"After the death of her husband, a Senate candidate, Natalie opted to run in his place. After a rapid rise as a political star, she now finds herself the newly elected vice president of the United States," TNT said. "Initially apprehensive that her job will be ceremonial in nature, she soon learns that it comes with a Top Secret duty: protecting the Constitution in times of great crisis with the aid of her Chief Steward and a secret operative designated Agent X."