How can a very old star be formed among Population III stars?
Many astronomers and cosmologists conjecture that Population III stars were very massive, perhaps even extremely massive. While this opinion is not universal, it does appear to be dominant. If this is the case, at least some of the very first stars died shortly after they formed, within a million years or less. This in turn would have meant the seeds for the first Population II stars would have been present in some places shortly after the very first stars formed and then died.
The Population III stars did not all form (and die) at the very same time, and those seeds needed to create the first Population II stars would not have been dispersed uniformly. So at least for some period of time in the early history of star formation, there would have been a mix of Population III stars in some places, Population II stars in others.