The General Calendar of the Roman Rite is primarily focused on canonized saints, holy men and women who lived either during or after Jesus' life on earth.
However, there is a tradition in the Church of also celebrating the lives of "biblical saints," holy individuals who lived before Jesus' incarnation.
Such is the case of St. Elisha, the successor to St. Elijah in the Old Testament.
The prophet Elisha is first mentioned in 1 Kings 19:16. He becomes a disciple of Elijah after he is seen plowing and Elijah places his mantle on him (1 Kings 19:19). Elisha leaves everything to follow Elijah and learn how to be like him. Elisha was the messenger of God during the reigns of Jehu, Jehoahaz and Jehoash in Israel.
The Catechism of the Catholic Church affirms, “The patriarchs, prophets and certain other Old Testament figures have been and always will be honored as saints in all the Church’s liturgical traditions” (CCC 61).
Carmelite calendar
Each religious order typically has its own liturgical calendar, which focuses on saints from their congregation.
One interesting feast the Carmelites celebrate is June 14, the memorial of St. Elisha (they also have a feast of St. Elijah on July 20).
The Carmelite Order explains some of the history of this feast on their website:
The Carmelite Order, mindful of its origin on Mount Carmel, with the liturgical celebration of the great Prophets Elijah and Elisha, intends to perpetuate the memory of their presence and of their works. This is why in the year 1399 the General Chapter decreed the celebration of the feast of Saint Elisha. In our time the Prophet gives effective witness of the prophetic Charism by means of fidelity to the true God and the service to his people.
Carmelites trace their origins to the disciples of Elijah and Elisha, who lived on Mt. Carmel as hermits for hundreds of years.
In addition to the Carmelite calendar, many Eastern Catholics and Orthodox Christians include the feast of the Holy Prophet Elisha on June 14.