National Climate Emergency Act of 2021 or the Climate Emergency Act of 2021 This bill directs the President to declare a national emergency relating to climate change. Further, the President must ensure that the federal government invests in projects to mitigate the emergency and reduce greenhouse gas emissions. At least 40% of such investments must be for historically disadvantaged communities. In addition, the President must ensure that the federal government reinvests in existing public sector institutions and creates new public sector institutions to strategically mobilize and channel investments at the scale and pace required by the emergency.