I rarely agree with Stubborn, but I must here. The consummation of the world means the end of the world.
If someone says X will last until the end of time, they mean it will last until the final moment of existence - not that it will cease to exist when the Apocalypse commences.
But that same someone
is the Vatican Council which does not say
"until the end of time". There is a poor translation which says "until the end of time", but that's not the Vatican Council. The Vatican Council, the someone
, says "usque ad consummationem saeculi" - until the consummation of the world.
In Mt 24 the disciples ask Our Lord: and what shall be the sign of thy coming, and of the consummation of the world?
And the answer of the Lord is that several things will happen until finally the gospel will have been preached all over the world, and then the consummation will come. Then, when we see the abomination of desolation, then the consummation will happen. Then we should read Daniel, watch out, run away, etc.
The abomination of desolation signals the beginning of the End Times, but Vatican I more likely suggests that the Papacy will remain until the end of the End Times(i.e the exact moment the world ends) rather than merely the beginning of the End Times. This is further supported by the fact that the "gates of Hell shall not prevail against Her" promise is not qualified with any "until the End Times" or "until the abomination of desolation" or anything similar.
Yes, the "gates of hell"-promise is not limited until the consummation. The gates of hell shall never prevail. But the "gates of hell"-promise does not concern shepherds or the Pope. The Council of Trent teaches that "the gates of Hell shall not prevail against her" means that the gates of hell won't prevail against the Faith as defined in the Creed of the same Council:
For which cause, this council has thought good, that the Symbol of faith which the holy Roman Church makes use of, –as being that principle wherein all who profess the faith of Christ necessarily agree, and that firm and alone foundation against which the gates of hell shall never prevail,– be expressed in the very same words in which it is read in all the churches. Which Symbol is as follows: [...]https://www.papalencyclicals.net/councils/trent/third-session.htm
The idea that "the gates of Hell shall not prevail" is a statement concerning the papacy is pure fantasy.
It's better to stick to the clear, authoritative, and definitive teachings of the Council of Trent and the Vatican Council than to invent contradicting ideas out of thin air.