The pasuk says אריה שאג מי לא יירא, when the lion roars who is not scared. Encoded in the term אריה is אלול, ראש השנה, יום כפור, הושענה רבה, as these are the days of the lion. Who is not scared during these days of אלול and תשרי. An allusion to this is found in the pasuk Amos 3:8. Shelah, Mesachta Rosh Hashana. The term ימים נוראים simply means Awesome Days, referring to Rosh Hashana and Yom Kippur. An alternate explanation is that it is days of Yirah, meaning days where we can acquire Yiras Shamayim, as this is what permeates the atmosphere at that juncture.
Devarim 6:13. Fear can spur one to be greater and accomplish more. An example of this in the physical world is a woman who will move a car to save her child. את תירא אלקיך 'א: את refers to לולא and שרית. These are days specifically of יראה.
The gemara tells us that on Rosh Hashana נפקדה שרה רחל וחנה, Sarah, Rachel and Chana were remembered by Hashem and it was decreed they would have children. This means on Rosh Hashana we have the qualities of their offspring—Yitzchak, Yosef and Shmuel—that of יראה.
Where do we see that Yitzchak, Yosef and Shmuel are associated with יראה?
1. Yitzchak: Yitzchak’s trait is that of דין, יראה.
2. Yosef: We are taught in the same gemara where it says נפקדה שרה רחל וחנה that Yosef was released from prison on Rosh Hashana for מלכות, kingship. מלכות is of course connected to יראה, as it says this in reference to a king. Additionally, a king puts fear into the people as we are instructed to daven for the welfare of the government because if not for people’s fear of it, each person would swallow his fellow alive. On Rosh Hashana we say מלכיות. So we see the connection of מלכות to יראה.
3. Shmuel: Shmuel also has this quality as he is the one who anointed Dovid as king.
The Sefas Emes points out a fascinating allusion. We know that Rosh Hashana is referred to as יום הדין. Let us take the hidden letters of the word דין which are דלת, יוד, נון. The gematria of these letters is 496, which has the same sum as מלכות (the source of יראה is in דין).
Fear of Hashem brings true happiness as in אשרי אדם מפחד תמיד, praiseworthy is the man who always fears. With this, we can understand why it says וגילו ברעדה עבדו את ה' ביראה, serve Hashem with awe and rejoice with trembling, as these two (yirah and rejoicing) are not a contradiction. Similarly, it states in Tanna Dvei Eliyahu שמחתי מתוך יראתי, I am happy amidst fear. This also gives us an appreciation of why the name יצחק, who embodies יראה, is rooted in צחוק, laughter, happiness. Let us take advantage of the opportunity when we ask for fear of Hashem—ךובכן תן פחד.
R' Aryeh Finkel (1931-2016) asked how we can fear Hashem and also be happy (which is what we are commanded to do)? Fear and joy are opposites! He answered that fear of Hashem gives us a context for understanding why we should be overjoyed with the opportunity to do mitzvos. When one appreciates that Hashem gives us our existence and every action we do has tremendous importance and ultimately determines our very eternity, how can we not be excited with the privilege to serve Hashem through the mitzvos? When one fears the calamity of missing the chance to actualize his very existence, he will be overjoyed with the opportunity that each mitzva presents.
