I will raise up for myself a faithful priest, who shall do according to my heart and mind; I will establish a lasting house for him and he shall walk before me all his days.
It’s a very interesting choice as it concludes a rebuke of the priest Eli in verses 27-36 of that chapter. Placing this in context, it follows Hannah’s song of thanksgiving (1 Samuel 2:1-10) for finally giving birth to a son, and that same son’s reception as a boy, this oracle about his mentor:
I am about to do something in Israel that will make the ears of everyone who hears it ring. On that day I will carry out against Eli everything I have said about his house, beginning to end. I announce to him that I am condemning his house once and for all, because of this crime: though he knew his sons were blaspheming God, he did not reprove them. Therefore, I swear to Eli’s house: No sacrifice or offering will ever expiate its crime. (1 Samuel 3:11-14)
Given the current context of sex abuse cover-up, I’d have to say this is a pretty chilling indictment if there’s any connection in the mind of God to the days of Eli’s sons.
That said, the occasion of sede vacante (which applies to a diocese as well as the papacy) is an important time for prayer. The collect for this Mass sums it up well, we pray to our “eternal shepherd” for a “pastor … who will please you by his holiness and to us show watchful care.”
As for Scriptural texts to go with the above antiphon and that from John 15:16 for Communion (I chose you and appointed you to go and bear fruit, says the Lord, fruit that will last.) I would suggest Isaiah 42 or Isaiah 61 two lyrical passages attributed or used by the Lord Jesus. I think they fit the context of the prayer intention of the church as well as the passages selected for the antiphon.
Remember that in the GIRM, sections 368-378 cover the universal regulations on the use of Masses for Various Needs and Occasions. You can this site’s brief comments here and here and here. The USCCB’s text on the VNO is here.