Veterans' Pathway to Citizenship Act of 2021 This bill waives certain requirements for eligible noncitizens seeking U.S. citizenship through service in the Armed Forces and addresses related issues. Currently, a noncitizen who served honorably during a designated period of hostilities may acquire citizenship on an expedited basis, subject to certain requirements. Under this bill, such a noncitizen shall be deemed to be a lawful permanent resident and to have fulfilled all residency and physical presence requirements for naturalization purposes if that noncitizen meets all other naturalization requirements. In addition, for such a noncitizen seeking naturalization, any prior removals from the United States shall not affect the noncitizen's eligibility for any immigration benefit or in determining whether the alien is deportable or inadmissible. Similarly, if such a noncitizen has received a pardon for an offense, that offense shall not affect the noncitizen's naturalization application unless the pardoned offense led to the noncitizen's separation from the Armed Forces in any manner other than honorable. Furthermore, when a noncitizen becomes eligible for naturalization through military service during hostilities, the Department of Homeland Security shall notify the noncitizen and submit an application on the noncitizen's behalf, unless the noncitizen requests otherwise. If a noncitizen is eligible for citizenship through this path but had filed an untimely application, that application shall be treated as timely and reviewed. This provision shall be in effect for a one-year period starting from this bill's enactment.