Yes. It is connected to, and built upon, the dispensation begun by Joseph Smith, but it is nonetheless new. We honor those in the LDS Church who have preserved what they have of Joseph Smith’s teachings, and Christ’s words through him. John the Baptist’s priesthood reckoned from the Jews he wrested the keys from. His priesthood continued, as did Christ’s and the apostles, despite the demise of the Jewish council, synagogues, and temple.
Denver Snuffer has ushered in the dispensation of the last times for the Gentiles, as John the Baptist ushered in the dispensation of the last times for the Jews (D&C 27:13). Joseph Smith’s inauguration of a dispensation of last times was abortive, and thankfully so. The Gentiles were given more time before their kingdoms were destroyed, as the use of those keys were started by Joseph Smith for the purpose of building the latter-day Zion. Zion was not built. Joseph Smith ushered in the dispensation of the fulness of times (D&C 128:18), which is a restoration that gathers all things in one, just as Moses did to start his dispensation. This dispensation of Joseph’s was incomplete. We have not received the vision of the revelation of all things given to the brother of Jared, nor the return of the priesthood that the Lord promised to Adam would return in the last days (Moses 6:7). The dispensation of the last times, which is the last time the Lord will prune His vineyard (Jacob 5:62), builds upon and completes the dispensation of the fulness of times, which gathers in one all things; or it could be said the last times completes the prior dispensation so the fulness of all things can be ushered in. The unfinished parts of the Restoration will be picked up and completed and built upon. Joseph’s success was marvelous but not exhaustive. It remains to be completed in another “last times” and “fulness of times” attempt, and the choice is ours to rise up. These are keys that can be implemented whenever God commands, and not conforming to Western definition notions. The dispensation attempt is finalized as the “last times” when it accomplishes what was begun with the turning of the keys to begin it: It becomes the “last times” for the kingdoms that the dispensation is opposed to. When the kingdoms fall of their own accord as they dash to pieces against the rock that is established, then the dispensation will be a success, and earn the title indefinitely in history (see D&C 39:17, where the Lord implores the Saints to be faithful that they may prune the vineyard for the last time). Otherwise, the last times will begin anew with a future generation. Likewise, for the fulness of times, if all things are not gathered in one, then it remains to be completed by another generation who can gather all knowledge, dispensations, glory, and keys into Zion.
All things are relative. Again, in another cycle, there will be other dispensations of last times and fulness of times. They are the ingathering of the harvest, and the burning of the field that happens every season before the long winter, where the Lord’s people are called to dwell in booths as covert from the storm. Moses and John the Baptist are bookends, just as Joseph Smith and Denver Snuffer are, only in the Lord’s strange act, the time has been shorter as the Lord has cut short His work in righteousness (D&C 52:11), as he has caused to be prophesied before (Romans 9:28). We pray for more time to accomplish what we need to accomplish, and that more might be saved.
To say “now is the time which is the dispensation of the last times, and the fulness of times,” is to say the kingdom of heaven is at hand now as well (Matthew 10:7). Today is another of those days.
Another take on the “last times” meaning is that it is the “latest” dispensation, and not the final one, as in Joseph Smith’s usage of “last of all” in D&C 76:22.