The expression do not be afraid
is a popular expression especially in connection with angelic appearances. We have it here in Luke 1:13 and also in Luke 1:30 (see also Matthew 1:20; Matthew 14:27; Matthew 28:10; Luke 2:10; Luke 5:10; Luke 8:50; Luke 12:32; and many more references). The angel announces that Zechariah and Elizabeth will have a son in their old age. His name is to be John
meaning, The Lord is gracious.
13 But the angel said to him, “Do not be afraid, Zechariah, for your prayer has been heard, and your wife Elizabeth will bear you a son, and you shall call his name John.