How do I offer prayers for the continued holiness of the clergy? 

The most powerful way to offer prayers to Jesus for the continued holiness of the clergy is during the Sacrifice of the Mass. The reason why the Mass is so powerful, is because by the ministerial priesthood, through the power of the Holy Spirit, Jesus re-presents the Paschal Mystery (Christ's passion, death, resurrection and ascension into Heaven) in an unbloody manner by transforming bread and wine into His Body, Blood, Soul and Divinity! Simply put, the sacrifice of Jesus on the cross and the offering of bread and wine are one single sacrifice, making the Mass to be the most powerful and perfect instrument for us to offer prayers to God the Father, and for us to receive graces from the Holy Spirit. Since the sacrifice of Jesus has so much power, when we unite our prayers to Christ's offering of Himself at Mass, the Eternal Father will see our prayer intentions as His Son's, and will not reject the prayer intentions, because He always accepts the perfect sacrificial offering of His only begotten Son, Jesus Christ, the Eternal High Priest  (CCC-1366; CCC-1364; CCC-1365; CCC-1404; CCC-1367; CCC-1373; CCC-1374; CCC-1375; CCC-1412; CCC-1324; Romans 12:1; 1 Peter 2:4-5; Live...The Holy Mass-Visions and Testimony of Catalina Rivas of Cochabamba, Bolivia; CCC-1368; CCC-1369; Lumen Gentium 10; Lumen Gentium 11; Lumen Gentium 28; Paragraph 13 of ECCLESIA DE EUCHARISTIA by Pope John Paul II; excerpt of Christ the High Priest by St. Fulgentius of Ruspe; Paragraph 8 of DOMINICAE CENAE by Pope John Paul II).