Higher Education Standards Improvement Act This bill requires states to take certain actions related to their oversight of institutions of higher education (IHEs). Specifically, states must (1) evaluate each IHE to determine if it meets standards for facilities, equipment, program length, and other relevant factors for a student to receive a professional license from the state; (2) accept and report student complaints that present consistent allegations with respect to an IHE; and (3) establish policies and procedures to anticipate and respond to the closure of an IHE. Such policies and procedures shall include maintaining sufficient cash reserves to ensure the repayment of any required refunds, a plan to ensure custodial record-keeping of institutional records and student transcripts, and the maintenance of contact information to ensure direct communication between the state and each student in the event of an IHE closure.