Promoting Readiness in Education to Prevent Additional Remediation and Expense Act This bill establishes grants and subgrants to address rates of postsecondary remediation. Specifically, the bill requires the Department of Education (ED) to award grants to states for certain activities, including aligning high school graduation requirements with entrance requirements for credit-bearing coursework in institutions of higher education (IHEs); developing statewide articulation agreements between IHEs and local educational agencies (LEAs); developing statewide standards for student placement in remedial coursework based on multiple indicators, including grade point average and completion of high school courses; and providing monitoring, training, technical assistance, and capacity building to entities receiving subgrants. States receiving such grants must award subgrants to partnerships between LEAs and IHEs. Entities receiving such subgrants must use funds to develop and implement programs and activities that improve high school education to prevent remedial education at the postsecondary education level, including activities related to advanced coursework and summer bridge programs; and strengthen remedial education at the postsecondary education level, including activities related to corequisite courses, technology-enhanced diagnostics and delivery of remedial education, and additional supports for certain students. The bill directs ED and the Institute of Education Sciences to contract with a third party to conduct an independent evaluation of the policies and services provided by the bill. The bill also specifies reporting requirements.