The phrase "In the days of" is used to indicate a new event. Alternate translation: "During the time that King Herod ruled over Judea" (See: [[rc://en/ta/man/translate/writing-newevent]])
"there was a particular" or "there was a." This is a way of introducing a new character in a story. Consider how your language does this. (See: [[rc://en/ta/man/translate/writing-participants]])
It is understood that this refers to the priests. Alternate translation: "division of priests" or "group of priests" (See: [[rc://en/ta/man/translate/figs-explicit]])
"who descended from Abijah." Abijah was an ancestor of this group of priests and all of them were descended from Aaron, who was the first Israelite priest.