Protection of Saudi Dissidents Act of 2021 This bill imposes temporary limits on arms sales to Saudi Arabia and requires various reports and actions related to the death of Saudi Arabian journalist Jamal Khashoggi. The President may not transfer or authorize for export certain defense articles or services to Saudi Arabia for 120 days after this bill's enactment. The prohibition shall remain in effect for up to three years unless the President periodically certifies to Congress that Saudi Arabia has not conducted (1) forced repatriation, intimidation, or killing of dissidents in other countries; (2) unjust imprisonment in Saudi Arabia of U.S. citizens or lawful aliens; or (3) torture of detainees in custody of the government of Saudi Arabia. The President shall certify to Congress that individuals with Saudi diplomatic credentials are not using such credentials to track or harass Saudi nationals in the United States. If the President does not make such a certification, the President shall close at least one Saudi diplomatic or consular facility in the United States until the certification is made. The bill requires reports to Congress on (1) whether any Saudi officials have engaged in a consistent pattern of harassment against any individual in the United States, and (2) whether the intelligence community fulfilled its duty to warn Khashoggi of the threats to his life.