Veteran and Beginning Farmers Assistance Act of 2021 This bill extends through FY2028 and makes other changes to a technology transfer program for assisting agricultural producers in rural areas. Among the changes, the bill (1) incorporates a specific focus on beginning, socially disadvantaged, and veteran farmers and ranchers; and (2) expands the scope of the assistance to include improving farm viability, strengthening supply chains, and increasing resilience to extreme weather through conservation practices.