Any time there's spread there's a chance of mutations, since it occurs during the reproduction of organisms. Since the Delta variant and the emerging Lambda variant can evade current vaccines pretty well, the vaccinated will for sure contribute to the emergence of more variants.
Eventually, though, pathogens will evolve to a point where they're infectious but not deadly. After all, the driving force behind mutations (or more precisely, the survival and multiplication of mutant variants) is survival, and killing the host isn't really conducive to that.
What this means is that we only really need protection from vaccines up to that point. After COVID becomes like any other coronavirus, which is infectious but not deadly, then we won't really need vaccines anymore.