[6] Grech studied philosophy at St. Mark's Priory, Rabat, Malta, and theology in St. Monica's College, Rome.

During the 1963 Papal conclave, he heard Giovanni Battista Montini's confession a couple of hours prior to his election as Pope Paul VI.

Agostino Trapè, Grech founded the Patristic Institute Augustinianum attached to the Lateran University in Rome[2] and served as its president from 1971 to 1979.

[13] He was created a cardinal deacon by Pope Benedict XVI in a consistory on 18 February 2012 and assigned the titular church of Santa Maria Goretti.

He raised the issue of how the Church hierarchy was handling the sexual abuse crisis: "Today many people are not able to come to believe in Christ because his face is obscured or hidden behind an institution that lacks transparency.

"[15][16] When Pope Francis marked the 50th anniversary of the founding of the Augustinianum, he praised Grech for the "grandiose simplicity" his sermons had achieved in his old age.