en_tn/luk/08/41.md

one of the leaders of the synagogue

"one of the leaders at the local synagogue" or "a leader of the people who met at the synagogue in that city"

fell down at Jesus's feet

Possible meanings are 1) "bowed down at Jesus's feet" or 2) "lay down on the ground at Jesus's feet." Jairus did not fall accidentally. He did this as a sign of humility and respect for Jesus. (See: rc://en/ta/man/translate/translate-symaction)