Answer:
They had to swear loyalty to the Greek leader.
Step-by-step explanation:
The Hellenistic period started after the conquests of Alexander the Great, who conquered a stretch of land from Greece to India.
After the death of Alexander, these lands were divided into several Hellenistic kingdoms. These kingdoms were dominated by a Greek leader, to who the inhabitants of these territories had to swear loyalty.
For example, in Egypt, a Greek dynastic, the Ptolemaic dynasty emerged. Cleopatra, the last ruler of Ancient Egypt, was in fact of Ancient Greek origin.