Here's how I understand it... I am fairly in agreement with what William Kelly has to say regarding "the four beasts" in his commentary on Daniel 7... quoted in part here:
[quoting Wm Kelly]
"It is plain, that whatever has fallen upon the Roman empire in past times, has been the ordinary course and decline of a great nation. Barbarian hordes tore it up, and separate kingdoms were formed. But prophecy tells us of another thing altogether. It warns of a judgment that disposes of the beast in a totally different way, and in contrast with the others. "I beheld till the beast was slain, and his body destroyed, and given to the burning flame. As concerning the rest of the beasts, they had their dominion taken away: yet their lives were prolonged for a season and time." That is, the remains of the Chaldeans, or of the races that were called so, we have still. Persia abides a kingdom, and the Greeks have lately become one. They exist, therefore, though not as imperial powers. We have these races of men, more or less, representing those powers; smaller, it is true, and no longer having dominion as empires. This is the meaning of ver. 12. Their dominion was taken away as rulers of the world, but "their lives were prolonged for a season and time." In this last empire, when the hour of its judgment comes, the fact is far otherwise. In the case of the first three beasts, they lost their imperial dignity, but themselves might be said to exist. But in the case of the fourth empire, the hour when its dominion is destroyed is the same hour in which it is itself destroyed. "The beast was slain, and his body destroyed, and given to the burning flame." Who can doubt that this is the same scene that we have alluded to in Rev. 19, where we are told, "And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against Him that sat on the horse, and against His army"? The prophet had come to the last beast."
-- William Kelly, Commentary on Daniel 7 - Daniel 7 William Kelly Major Works Commentary (biblehub.com)
[end quoting; bold and underline mine]
____________
I think it is a major mistake to think that just because Rev13 DESCRIBES the final beast as "LIKE unto a LEOPARD, and his FEET were AS the feet of a BEAR, and his MOUTH AS the mouth of a LION..." that this somehow means all the previous beasts were also present at that [future] time (and THEN [supposedly at that FUTURE time] their lives were prolonged for a season and time, Dan7:12 [i.e. prolonged so that these humans [unsaved] supposedly ENTER the MK age, as some have suggested], rather than its saying something like (as we often say), "the kid has his grandfather's swift feet, and the same notch in his left ear that his father has..." (etc etc), in Rev13:2... and Daniel's (in 7:12) referring to the [NOW-] PAST kingdoms [/empires, or whatever] as having been ended, "yet their lives were prolonged for a season and a time" BACK THEN when they existed (not "future," as some suppose Dan7:12 to be saying).
Make sense? = )
[quoting Wm Kelly]
"It is plain, that whatever has fallen upon the Roman empire in past times, has been the ordinary course and decline of a great nation. Barbarian hordes tore it up, and separate kingdoms were formed. But prophecy tells us of another thing altogether. It warns of a judgment that disposes of the beast in a totally different way, and in contrast with the others. "I beheld till the beast was slain, and his body destroyed, and given to the burning flame. As concerning the rest of the beasts, they had their dominion taken away: yet their lives were prolonged for a season and time." That is, the remains of the Chaldeans, or of the races that were called so, we have still. Persia abides a kingdom, and the Greeks have lately become one. They exist, therefore, though not as imperial powers. We have these races of men, more or less, representing those powers; smaller, it is true, and no longer having dominion as empires. This is the meaning of ver. 12. Their dominion was taken away as rulers of the world, but "their lives were prolonged for a season and time." In this last empire, when the hour of its judgment comes, the fact is far otherwise. In the case of the first three beasts, they lost their imperial dignity, but themselves might be said to exist. But in the case of the fourth empire, the hour when its dominion is destroyed is the same hour in which it is itself destroyed. "The beast was slain, and his body destroyed, and given to the burning flame." Who can doubt that this is the same scene that we have alluded to in Rev. 19, where we are told, "And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against Him that sat on the horse, and against His army"? The prophet had come to the last beast."
-- William Kelly, Commentary on Daniel 7 - Daniel 7 William Kelly Major Works Commentary (biblehub.com)
[end quoting; bold and underline mine]
____________
I think it is a major mistake to think that just because Rev13 DESCRIBES the final beast as "LIKE unto a LEOPARD, and his FEET were AS the feet of a BEAR, and his MOUTH AS the mouth of a LION..." that this somehow means all the previous beasts were also present at that [future] time (and THEN [supposedly at that FUTURE time] their lives were prolonged for a season and time, Dan7:12 [i.e. prolonged so that these humans [unsaved] supposedly ENTER the MK age, as some have suggested], rather than its saying something like (as we often say), "the kid has his grandfather's swift feet, and the same notch in his left ear that his father has..." (etc etc), in Rev13:2... and Daniel's (in 7:12) referring to the [NOW-] PAST kingdoms [/empires, or whatever] as having been ended, "yet their lives were prolonged for a season and a time" BACK THEN when they existed (not "future," as some suppose Dan7:12 to be saying).
Make sense? = )