Ushering Progress by Leveraging Innovation and Future Technology Act of 2021 or the UPLIFT Act of 2021 This bill requires the Small Business Administration (SBA) to establish the Innovation Centers Program for providing assistance to startups and new or growing small businesses. Under the program, the SBA may enter into cooperative agreements to provide financial assistance to historically Black colleges and universities, minority-serving institutions, and community colleges. Such entities must then undertake five-year projects operating as an innovation-focused small business accelerator or incubator. These projects must involve working with underserved groups, include the joint provision of programs and services by the entities and the SBA, and ensure participating small businesses have access to regulatory information that affects them.