Palestinian International Terrorism Support Prevention Act of 2021 This bill imposes sanctions targeting Hamas, the Palestinian Islamic Jihad, and any affiliate or successor groups. The President shall periodically report to Congress a list of each foreign person or instrumentality that knowingly assists, provides significant support or services to, or is involved in a significant transaction with a senior member or supporter of any of the targeted groups. The President shall impose two or more sanctions on the named persons. Specifically, the person may be (1) denied credit and services from the Export-Import Bank, (2) barred from purchasing certain controlled defense articles, (3) denied exports of items on the U.S. Munitions List, (4) prevented from receiving exports of certain goods or technology controlled for national security reasons, (5) prohibited from receiving financing of more than $10 million from any U.S. financial institution, or (6) subject to property-blocking restrictions. The President shall periodically report to Congress a list of foreign governments that have repeatedly provided material support for the targeted groups' terrorist activities. The President shall bar these governments from receiving for one year (1) U.S. assistance, or (2) exports of controlled munitions. The Department of Treasury shall instruct U.S. leadership of international financial institutions to oppose the provision of assistance to an identified government for one year. The bill provides for certain exceptions and waivers, such as for transactions that would serve U.S. national interests. The President shall report to Congress and periodically provide briefings on other specified topics related to the targeted groups, such as where these groups secure financing and surveillance equipment.