Inspire to Serve Act of 2021 This bill establishes new and expands existing military and national service programs, and revises federal personnel provisions. The bill establishes programs relating to civic education and service learning, including by providing grants supporting these programs for grades K-12 and at institutions of higher education. The bill also establishes the Council on Military, National, and Public Service which must coordinate executive branch policies to promote and expand opportunities for military service, national service, and public service. The Office of Management and Budget must create an online recruitment portal for service organizations. Additionally, the bill expands military service programs, including by expanding the Junior Reserve Officers' Training Corps, establishing pre-service tuition grants in exchange for enlisted service commitments, and creating a pilot program for military departments to partner with community colleges and vocational schools to provide service members with access to technical education programs. Service programs are expanded by increasing the number of specified national service positions, increasing certain living allowances and stipends, and creating new fellowship programs. Federal personnel provisions are revised to, among other things, provide certain national service alumni with noncompetitive eligibility for federal employment.