Strengthening Local Processing Act of 2021 This bill revises provisions related to meat and poultry processing establishments, including smaller establishments (i.e., those with between 10 and 500 employees) and very small establishments (i.e., those with fewer than 10 employees or annual sales of less than $2.5 million). For example, the Department of Agriculture (USDA) must establish a searchable database of peer-reviewed validation studies for use in developing Hazard Analysis and Critical Control Points plans for smaller and very small establishments. The bill increases the maximum federal cost share from 50% to 65% that USDA may provide to assist states in creating meat and poultry inspection programs. Additionally, USDA must conduct outreach with states that have meat and poultry inspection programs, but that do not have Cooperative Interstate Shipment programs. The Cooperative Interstate Shipment program allows state-inspected facilities to operate as federally-inspected facilities and ship their products in interstate commerce and internationally. USDA must also award competitive grants for activities to adapt production, processing, distribution, and sales systems to respond to and recover from the effects of the COVID-19 pandemic, including activities that support (1) the health and safety of meat and poultry plant employees, suppliers, and customers; (2) increased processing capacity; and (3) the resilience of the small meat and poultry processing sector. Further, the bill establishes grant programs to (1) establish or expand career training programs at community colleges, vocational schools, and universities related to meat and poultry processing; and (2) support smaller and very small establishments by offsetting the cost of training new meat and poultry processors.