Adam Clarke on Luke 7:3

Elders of the Jews - These were either magistrates in the place, or the elders of the synagogue which the centurion had built, Luk 7:5. He sent these, probably, because he was afraid to come to Christ himself, not being a Jew, either by nation or religion. In the parallel place in Matthew, he is represented as coming to Christ himself; but it is a usual form of speech in all nations, to attribute the act to a person which is done not by himself, but by his authority.