High Speed Rail Corridor Development Act of 2021 This bill revises and reauthorizes through FY2025 the high-speed rail corridor development competitive grant program of the Department of Transportation (DOT). In awarding grants, the bill requires DOT to prioritize (1) projects that involve the purchase of electrified next generation passenger rail equipment, and (2) applications for projects that provide for a greater non-federal share of the cost of such projects. DOT must also for each fiscal year set aside 50% of funds for projects with a federal share that does not exceed 50% of the project net capital cost.