Emergency Security Supplemental Appropriations Act, 2021 This bill provides FY2021 supplemental appropriations for federal agencies to respond to the events at the U.S. Capitol Complex on January 6, 2021, and assist Afghan refugees. It also provides supplemental appropriations for the legislative branch to address COVID-19 and modifies requirements for certain programs that provide special immigrant status to eligible nationals of Afghanistan or Iraq, TITLE I--DEPARTMENT OF DEFENSE This title provides appropriations for the National Guard to respond to the events at the U.S. Capitol Complex on January 6, 2021, and for related purposes. The title also provides appropriations to the Department of Defense for overseas humanitarian, disaster, and civic aid. TITLE II--DEPARTMENT OF HEALTH AND HUMAN SERVICES This title provides appropriations to the Administration for Children and Families for refugee and entrance assistance activities. The funding must be used for activities for Afghan individuals within the United States who have been granted special immigrant status. TITLE III--LEGISLATIVE BRANCH This title provides appropriations for the legislative branch to respond to the events at the U.S. Capitol Complex on January 6, 2021, and address COVID-19. Specifically, the title provides appropriations for the Senate, the House of Representatives, the U.S. Capitol Police, U.S. Capitol Police Mutual Aid Reimbursements, and the Architect of the Capitol (AOC). The title also provides appropriations for payments to the widows and heirs of deceased Members of Congress, including (1) Susan M. Wright, widow of the late Representative Ronald Wright; and (2) the heirs of the late Representative Alcee Hastings. (Sec. 301) This section designates the wellness program of the U.S. Capitol Police as the Howard C. Liebengood Center for Wellness. (Sec. 302) This section modifies the salary cap for the U.S. Capitol Police during 2021. (Sec. 310) This section prohibits funds from being used to install permanent, above-ground fencing around the perimeter, or any portion thereof, of the U.S. Capitol Grounds. (Sec. 311) With congressional approval, the AOC may accept contributions of, and incur obligations and make expenditures out of available appropriations for, supplies, products, and services necessary to respond to an emergency involving the safety of human life or the protection of property, as determined or declared by the Capitol Police Board. TITLE IV--BILATERAL ECONOMIC ASSISTANCE This title provides appropriations to the Department of State for migration and refugee assistance to address humanitarian needs in Afghanistan and to assist Afghan refugees. The title also provides appropriations to the State Department for the United States Emergency Refugee and Migration Assistance Fund. (Sec. 401) This section increases the number of special immigrant visas available to qualified Afghan nationals who worked for the U.S. government or a North Atlantic Treaty Organization (NATO) mission in Afghanistan, extends the deadline for applying for such visas, and relaxes certain qualifications. All applicants for such a visa must establish that the applicant was employed with the U.S. government or a NATO mission for one year, where currently some applicants must prove two years of employment. This section also eliminates a requirement that the applicant faces an ongoing serious threat in Afghanistan due to such employment. Furthermore, for an applicant qualifying for a visa by performing duties for U.S. military personnel stationed with a NATO mission, this section eliminates a requirement that the duties performed qualify as sensitive and trusted duties. This section also relaxes limits to appealing rejections for applications for such visas. (Sec. 402) This bill authorizes the State Department and the Department of Homeland Security (DHS) to jointly postpone the medical exam requirement for individuals seeking entry into the United States under the program described in Section 401. If an individual receives such a postponement, DHS shall ensure to the greatest extent possible that individual undergoes a medical exam no later than 30 days after admission into the United States. Such an individual's status as a lawful permanent resident shall be conditional until the individual undergoes the required medical exam. (Sec. 403) This section modifies the immigration benefits of the surviving family members of certain deceased individuals. The surviving spouse or child of a U.S. government employee abroad shall qualify as a special immigrant if that employee performed at least 15 years of faithful service or was killed in the line of duty. This section also expands surviving family member benefits for certain programs that provide special immigrant status to eligible nationals of Afghanistan or Iraq, including the program described in Section 401. Specifically, if an individual submitted an application to the Chief of Mission that included an accompanying spouse or child and that application would have been approved but for the individual's death, the surviving spouse or child shall remain eligible to receive a visa under the respective program. Currently, such survivor rights only apply if the deceased individual's petition was approved. (Sec. 404) If an individual has an approved petition under a program that provided special immigrant status to translators who worked for the Armed Forces in Afghanistan or Iraq but a visa is not immediately available, the State Department or DHS may convert that petition to an approved petition under another program which provides special immigrant status to certain Iraqi nationals, if there are visas available under that second program. (DHS and the State Department currently only have the authority to convert petitions filed before October 1, 2008.) TITLE V--DEPARTMENT OF JUSTICE This title provides appropriations to the Department of Justice (DOJ) for state and local law enforcement assistance. DOJ must use the funds for restoring funds that were used for extraordinary law enforcement and related costs directly associated with protection of the President-elect from November 4, 2020, until the inauguration of the President-elect as President. TITLE VI--GENERAL PROVISIONS--THIS ACT (Sec. 601) This section specifies that the funds provided by this bill are in addition to funds otherwise appropriated for the fiscal year involved. (Sec. 602) Funds provided by this bill may not remain available beyond the current fiscal year, unless this bill provides otherwise. (Sec. 603) Unless otherwise specified by this bill, the funds provided by this bill are subject to the authorities and conditions that apply to the applicable appropriations account for FY2021. (Sec. 604) This section specifies that funding provided by this bill may only be used for the purposes specifically described in the bill. The section includes an exception for funds used to restore amounts for obligations incurred prior to the date of the enactment of this bill. (Sec. 605) This section specifies that the term coronavirus in this bill means SARS-CoV-2 or another coronavirus with pandemic potential. (Sec. 606) This section provides that amounts designated by this bill as emergency requirements are only available (or rescinded or transferred, if applicable) if the President subsequently designates the amounts and transmits the designations to Congress. (Sec. 607) This section specifies that the emergency funds that are transferred pursuant to this bill retain the emergency designation.