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.
"His wife was descended from Aaron." This means she was from the same line of priests as Zechariah. Alternate translation: "His wife was also descended from Aaron" or "Zechariah and his wife Elizabeth were both descended from Aaron" (See: [[rc://en/ta/man/translate/figs-explicit]])