John Gill Commentary Luke 1:14

"And thou shalt have joy and gladness; and many shall rejoice at his birth." — Luke 1:14 (ASV)

And you shall have joy and gladness
Not only because of his having a son; but because this his son would be the prophet of the Highest; would go before the Lord, and prepare his ways; give knowledge of salvation to many, and light to them that were in darkness, and guide their feet in the way of peace:

all which, and more, he afterwards expresses in his song, whereby this part of the angel's prediction had its accomplishment:

and many shall rejoice at his birth;
as the neighbours and cousins of his parents did; see (Luke 1:58) and not only they, but all others, who, afterwards had knowledge of him as prophet, and as the forerunner of the Messiah.