Hello Mikra and Ιάκοβε
In modern Greek αρχή means 1. "start, beginning" and
αρχηγός means "leader, shief"
These two words have a common root, the ancient Greek verb "άρχω", which has a double meaning: 1. "make a start"
2. "govern, lead"
These two meanings ("make a start" and "lead") are different, but not irrelevant. A leader in ancient times (before democracy was established) was the person who decided and took initiative for many things, in other words he made a start of many issues concerning the state and the people.