Feast Day of Our Lord Jesus Christ Eternal High Priest - An Invitation for the whole Church to Contemplate the Priesthood of Christ and Pray for Priests!

As of 2014, the Church celebrates the feast of Our Lord Jesus Christ Eternal High Priest. This feast is celebrated on the Thursday after the Solemnity of Pentecost (June 1st in 2023). (See Prayers for Priests at Bottom)
The Feast of Our Lord Christ Eternal High Priest invites the whole Church to contemplate the priesthood of Christ. It encourages all believers in their commitment to imitate Jesus, especially those called to the ministerial priesthood. It is prayed that the priests may live their pursuit of personal sanctification in a total surrender to God and the Church.
Priesthood and Commitment to Holiness
The Feast of Christ Priest has been celebrated for several years in various religious institutions and countries. There is already a votive mass for it in the Roman Missal. 
In a letter to the Episcopal Conference, the Congregation for Divine Worship and the Regulation of the Sacraments in Rome indicated some time ago that it is possible to include this feast in the Church calendars.

The feast is also to be understood in line with the Annual Day of Prayer for the Sanctification of the Priest, established by Blessed John Paul II.

3 Prayers for Priests:

St. Therese of Lisieux’s Prayer for Priests - O Jesus, eternal Priest, keep your priests within the shelter of Your Sacred Heart, where none may touch them. Keep unstained their anointed hands, which daily touch Your Sacred Body. Keep unsullied their lips, daily purpled with your Precious Blood. Keep pure and unearthly their hearts, sealed with the sublime mark of the priesthood. Let Your holy love surround them and shield them from the world’s contagion. Bless their labors with abundant fruit and may the souls to whom they minister be their joy and consolation here and in heaven their beautiful and everlasting crown. Amen.

2. St.John Vianney’s Prayer for Priests

God, please give to your Church today many more priests after your own heart. May they be worthy representatives of Christ the Good Shepherd.
May they wholeheartedly devote themselves to prayer and penance;
be examples of humility and poverty; shining models of holiness;
tireless and powerful preachers of the Word of God; zealous dispensers of your grace in the sacraments. May their loving devotion to your Son Jesus in the Eucharist and to Mary his Mother be the twin fountains of fruitfulness for their ministry. Amen.

3. St. Pope John Paul II’s Prayer for Priests to Our Blessed Mother

Mother of Jesus Christ and Mother of priests, Accept this title which we bestow on you to celebrate your motherhood and to contemplate with you the priesthood of your Son and of your sons, O holy Mother of God. Mother of Christ, to the Messiah Priest you gave a body of flesh through the anointing of the Holy Spirit for the salvation of the poor and the contrite of heart; guard priests in your heart and in the Church,
O Mother of the Savior. 
Mother of Faith, you accompanied to the Temple the Son of Man,
the fulfillment of the promises given to the fathers;
give to the Father for his glory the priests of your Son,
O Ark of the Covenant.
Mother of the Church, with the disciples in the Upper Room
you prayed to the Spirit for the new People and their shepherds;
obtain for the Order of Presbyters a fullness of gifts, O Queen of the Apostles.

Mother of Jesus Christ, you were with Him at the beginning of His life and of His mission, you sought the Master among the crowd, you stood beside Him when he was lifted up from the earth consumed as the one eternal sacrifice, and you had John close by you, your son;
accept from the beginning those who have been called,
protect their growth, accompany your sons in their life and in their ministry, O Mother of Priests. Amen.

Sources: https://web.archive.org/web/20140714225535/http://rkkerk.nl/nieuws.php?id=54