On January 12, 2014, Pope Francis named Quevedo as one of 19 men to be inducted into the
College of Cardinals in the
consistory of February 22, 2014, with the titular church of
Santa Maria "Regina Mundi" a Torre Spaccata. and, until his 80th birthday, the second Filipino cardinal-elector, along with
Luis Antonio Tagle,
Archbishop of Manila. Pope Francis named him member in Pontifical Council for Justice and Peace and Pontifical Council for Inter-religious Dialogue. On November 6, 2018, Pope Francis accepted Quevedo's resignation as archbishop, and appointed
Angelito Lampon as his successor. Cardinal Quevedo ceased to be a cardinal-elector on his 80th birthday in 2019. Due to
COVID-19 pandemic travel restrictions and the vacancy of the
Apostolic Nunciature to the Philippines, Cardinal Quevedo installed
Charlie M. Inzon as the sixth
Apostolic Vicar of Jolo on April 4, 2020, and
Jose Cabantan as
Archbishop of Cagayan de Oro on August 28, 2020. ==Other posts==