This is what I am seeing, using the New Advent page for convenience:
- Zechariah is the high priest at the time when Mary is betrothed to Joseph in the temple at age 12 (chapters 8-9). A bit later, at the decision to have Mary spin the veil (chapter 10), it is said that he is dumb and cannot speak; therefore Samuel is serving in his stead. It is not said why Zechariah is dumb.
- Elizabeth is Mary's kinswoman (chapter 12), and she says that something leaps in her womb as Mary comes to visit her after having spun the veil. It is not said what or who is in her womb.
- Elizabeth hides John, named here for the very first time in the text, while Herod is carrying out the massacre of the innocents (chapter 22). John is introduced as if he needs no introduction.
- Zechariah is approached by Herod's men during their search for John, and they ask him where his son is (chapter 23); this is our first clue that Zechariah even has a son, let alone that the son is John, of the womb of Elizabeth, implying that Elizabeth is married to the high priest. Zechariah refuses to tell, and he pays the price for that refusal.