From Preparing for the Yom Hadin (#978) by Rabbi Avigdor Miller
Q: Should I go into Rosh Hashanah with simcha (happiness) because it is yom tov or with trepidation because it’s the yom hadin (Day of Judgment)?
A: You have to do both. “Gilu bi’rada — [you have to] tremble and rejoice.” It’s a yom tov, no question about it. But on Rosh Hashanah, the Gemara says the more he is afraid on Rosh Hashanah the better off he is.
Be afraid on Rosh Hashanah; very important. In the olden days, they wept on Rosh Hashanah. Jews wept on Rosh Hashanah. It’s very important to weep on Rosh Hashanah! Be afraid! It’s a yom hadin. But the most important purpose of that is in our minds we should get the idea we are standing before the great Judge.
It’s an ideal that we have to form in our mind: The cognizance, the awareness that Hashem judges the world, and He is the dayan, the King who rules everything. Even for a small trial, people are afraid. Imagine chas v’shalom they’re calling you for a small thing before a judge. When you come before the Great Judge, you can’t deceive Him. There the greatest fear is necessary, certainly. And the more fear you have on the yom hadin the more you’re succeeding in formulating your mind with the proper attitudes. In that may you can deserve to get a year of happiness and all the things you’re looking for.