Both Uses of

advent
in
The Scarlet Letter

It pained, and at the same time amused me, to behold the terrors that attended my advent, to see a furrowed cheek, weather-beaten by half a century of storm, turn ashy pale at the glance of so harmless an individual as myself; to detect, as one or another addressed me, the tremor of a voice which, in long-past days, had been wont to bellow through a speaking-trumpet, hoarsely enough to frighten Boreas himself to silence.
p. 15.3

advent = arrival

Such was the young clergyman's condition, and so imminent the prospect that his dawning light would be extinguished, all untimely, when Roger Chillingworth made his advent to the town.
p. 111.8 *

Definitions:

(1) (advent as in: the advent of)
an arrival or beginning -- especially of something important or significant
(2) (Advent as in: the first Sunday of Advent)
a Christian season that includes the four Sundays preceding Christmas (to celebrate the birth of Jesus)
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Less commonly, Advent can be the name of a place.