Health, Opportunity, and Personal Empowerment Act of 2021 or the HOPE Act of 2021 This bill establishes two Health, Opportunity, and Personal Empowerment (HOPE) pilot projects to improve economic security for individuals who meet income or other requirements. The Department of Health and Human Services (HHS), the Department of Agriculture, and the Department of Housing and Urban Development must collaborate on the projects. The first project provides awards to certain government entities to assist eligible individuals in establishing HOPE accounts through banks, credit unions, or governmental agencies. HOPE accounts must (1) provide access to specified financial services and information on public benefits, health insurance, and other topics; and (2) facilitate activities such as applying for government benefits and filing taxes. HHS must hold a competition to award contracts to private businesses and nonprofits to develop technology applications and other tools for HOPE accounts. The second pilot project provides grants that allow government and nonprofit organizations to enter voluntary agreements with eligible individuals to carry out long-term plans related to improving economic security and upward mobility.