The second Mass listed for Various Needs and Occasions is “For the Pope,” and this liturgy is designated “Especially on the Anniversary of Election.” Currently, the anniversary is March 13th, which will always be Lent.
There is an important rubric that precedes the given antiphons and prayers:
This Mass is said, with the color white, on the anniversary of the election of the Pope in places wherever special celebrations are held, provided they do not occur on a Sunday of Advent, Lent or Easter, on a Solemnity, on Ash Wednesday, or on a weekday of Holy Week.
This is one of the “top four” VNO Masses, in that it can replace an ordinary Sunday or any observance of a feast or any kind of memorial. The provision for using this Mass is “wherever special celebrations are held.” I suppose the home diocese of the Pope is a given, as would be the city of Rome. In my thirty-plus years of liturgical service, I’ve never been part of a celebration of a papal anniversary. Nor do I recall hearing of one taking place in ordinary parishes.
The given antiphons are Matthew 16:18-19 (You are Peter) for entrance and John 21:15, 17 (Do you love me more than these?) for Communion. Musing on the Psalm I might use with these, maybe the 40th. A New Testament canticle might be a better choice, or perhaps even the greeting in 1 Peter 1:3-9.
The Roman Missal give three options for the Collect, and I find none of them really strong. Best moment is in choice #1:
… grant that he … may be for your people a visible source and foundation of unity in faith and of communion.
Weakest in #3, where the prayer in its English translation speaks of God the Father as “shepherd of souls.”