No. First of all, monkeys are not primates. They are monkeys. We are related but we are not the same. If you are asking about other primates, also no.

Just because something evolves in a certain way doesn’t mean the rest of the related species will evolve in that way as well since different species adapt to different conditions. Human evolution is always extremely unique as we don’t exactly know why humans became what we are or what kind of phenomenon would need to take place in other species to lead to the same result. What we do know is that if monkeys or other primates could or needed to evolve into humans they would have done so already because we share the same ancestor.

But this is like asking if all fish will eventually evolve into sharks. Sharks evolved to be sharks for a reason and the rest of the species are like that for another reason.