Arctic Security Initiative Act of 2021 This bill requires the Department of Defense (DOD) to conduct an assessment and implement a program related to national security interests in the Arctic region. Specifically, the Commander of the United States Northern Command of DOD must consult and coordinate with specified defense entities to conduct an independent assessment with respect to the activities and resources required for FY2023-FY2027 to achieve specified objectives related to national security interests in the Arctic region. The assessment must focus on the activities and resources required to achieve the following objectives: the implementation of the National Defense Strategy and military service-specific strategies with respect to the Arctic region; the maintenance or restoration of the comparative military advantage of the United States in response to great power competitors in the Arctic region; the reduction of the risk of executing operation and contingency plans of DOD; and to maximize execution of DOD operation and contingency plans, in the event deterrence fails. Additionally, DOD must establish the Arctic Security Initiative program to enhance security in the Arctic region, to be informed by the assessment required by this bill. DOD must annually submit an unclassified future years plan, which may include a classified annex, for the activities and resources of the program that includes specified elements (e.g., a detailed time line for achieving requirements). The plan must also be included in budget materials submitted by DOD in support of the budget of the President for FY2023.