The word αριστεύς or άριστος in ancient Greek had these general meanings: excellent, perfect, superior, supreme, optimum.
αριστεύς or άριστος in ancient Greece usually referred to:
1) someone extremely brave in a battle (the bravest of all) or
2) someone belonging in the highest social class.
It is worth noting that the word "aristocracy" comes from the word "άριστος" (=from the highest social class) plus the word "κράτος" (=governing). This is different from "democracy", which is the governing (κράτος) by all citizens (δήμος) regardless of their social class.
In modern Greek we use the word "άριστος" with the meaning of "excellent", "perfect"
Example: Είναι άριστος μαθητής.= He is an excellent student.
As for the translations you found:
"excellent person" or "chef of a class" could be both acceptable.