Greater Leadership Overseas for the Benefit of Equality Act of 2021 or the GLOBE Act of 2021 This bill contains provisions related to (1) the protection of LGBTQI individuals globally; and (2) immigration protections for vulnerable individuals. The bill establishes (1) an interagency group to respond to urgent threats to LGBTQI people in foreign countries, and (2) a permanent Special Envoy for the Human Rights of LGBTQI Peoples in the Department of State. The President shall impose visa-blocking sanctions on foreign persons responsible for violating the human rights of individuals based on sexual orientation, gender identity, or sex characteristics. The State Department shall establish the Global Equality Fund to provide assistance to nongovernmental organizations working to advance and protect human rights. The U.S. Agency for International Development shall establish the LGBTQI Global Development Partnership to work with the private sector and nongovernmental organizations to support LGBTQI rights. The bill removes prohibitions against providing foreign assistance to nongovernmental organizations that offer certain medical services (e.g., abortion-related services) using non-U.S. government funds. The bill contains several immigration-related provisions, such as those establishing that persecution based on sexual orientation or gender identity may form the basis of an asylum request, allowing certain applicants to file asylum claims more than a year after their arrival in the United States, including a permanent partnership between two partners as a marriage for immigration law purposes, providing for free counsel in certain immigration proceedings, and granting U.S. citizenship to a child born abroad through assistive reproductive technology from a U.S. citizen who is the child's nonbiological parent.