Supporting Teachers with Residency Opportunities and New Grants Act of 2021 or the STRONG Act of 2021 This bill reauthorizes through FY2024 the Teacher Quality Partnership program and otherwise revises the program to allow certain undergraduate students with an academic major related to teaching to enter into teaching residency programs. (Currently, only recent graduates and certain mid-career professionals may participate in these programs.) In addition, the bill allows undergraduate students who enter into such a program to participate in the Public Service Loan Forgiveness program.