Bishop Elya, a native of Maghdouché, Lebanon, entered the Melkite Basilian Salvatorian Order, where he professed his solemn vows in 1949. After completing his philosophical and theological studies, Elya was ordained a priest on 17 February 1952. He later obtained a licentiate in theology from the Pontifical Gregorian University and taught moral theology and philosophy in the Monastery of Saint Savior in Lebanon and served as rector of the seminary of Saint Basil in Methuen, Massachusetts.