John Lightfoot on Matthew 9:18

[Behold, a ruler.] Distinction is made between the bishop of the congregation, and the head of the congregation. For while the discourse is there of the high priest reading a certain portion of the law on the day of Expiation agreeable to the day, thus it is said, The bishop of the synagogue takes the book of the law, and gives it to the ruler of the synagogue. Where the Gloss thus, "The synagogue was in the mount of the Temple, near the court [which is worthy to be marked]: The Chazan [or bishop, or overseer] of the synagogue is the minister: and the ruler of the synagogue is he by whose command the affairs of the synagogue are appointed; namely, who shall read the prophet, who shall recite the phylacteries, who shall pass before the ark."

Of this order and function was Jairus, in the synagogue of Capernaum: so that the word ruler, being understood in this sense, admits of little obscurity, although one, or a certain, be not there: "he speaking these words, 'Behold, the ruler of that synagogue,'" &c.