From 1982 to 1987, Pepe served as professor of canon law at St. Charles Borromeo Seminary. He was also appointed vice-chancellor (1987) and chancellor (1990) of the archdiocese; during his tenure in the chancery, he served as vice-promoter for the cause of beatification of Katharine Drexel.[2]
On October 18, 2003, Pepe dedicated the Our Lady of LaVang Vietnamese Catholic Community in Las Vegas as a shrine. In 2004, he opened a diocese human resources department along with an Office of Hispanic Ministry, an Office of Liturgy and Worship and an Office of Archives. On September 27, 2007, Pepe dedicated Bishop Gorman High School in Las Vegas.[3]
On November 2, 2007, a priest appointed by Pepe to Our Lady of Las Vegas Catholic Parish was sentenced to four to 12 years in state prison for assault. Reverend George Chaanine had assaulted and groped Michaelina Bellamy, the events coordinator at the church, then evaded arrest for six months. Bellamy's injuries from the assault included a broken hand and two large gashes in her head. Chaanine later claimed to be in love with Bellamy and investigators found evidence that he provided her with financial support.[4]
On February 28, 2018, Pope Francis accepted Pepe's letter of resignation as bishop of the Diocese of Las Vegas after he reached the mandatory retirement age of 75.[2]