We Proclaim God is King on Rosh Hashanah: What About the Rest of the Year?

Recite before Me on Rosh Hashanah [texts making mention of] kingship, remembrance, and the shofar-- kingship, so that you may proclaim Me king over you; remembrance, so that your remembrance may rise favourably before Me; and through what? Through the shofar. (Rosh Hashanah 16a)

Is it only on Rosh Hashanah that we have kabalas ‘ol malkhus shamayim?

The Imrei Emes of Ger says, true, that is an obligation all year. However, Rosh Hashanah gives us the power to do it all year.

As the Gemara expresses it:
R. Zevid said: If the first day of the New Year is warm, all's the year will be warm; if cold, all the year will be cold. Of what [religious] significance is this [weather forecast]? (Bava Basra 147a)

The Imrei Emes explains the Gemara metaphorically:
The degree of warmth and excitement with which we accept malkhus shamayim on Rosh Hashanah – is the degree of warmth and excitement with which we serve God all year.

Rosh Hashanah that Falls on Shabbos: Is Writing Permitted?

Once, when Rosh Hashanah occurred on Shabbos, R. Levi Yitzchak of Berditchev made the following argument to God:
-- Master of the universe, this year You are forced to inscribe Your people Israel for a good and peaceful year. Since it is, shabbos ha’yom l’Hashem, Shabbos today for Hashem, and writing is forbidden, how can you fulfill: b’rosh Hashanah yi’ka’seivun? On Rosh Hashanah will be inscribed...? You have no choice but to inscribe each one of your children to life because pikuach nefesh dokheh shabbos, saving a life overrides shabbos…and writing then becomes permitted.

True Kavanah During Shofar Blowing

R. Levi Yitzchak of Berditchev was looking for a Ba’al Toke’ah for his Beis Medrash. Candidates came from all over for the honorable position.

R. Levi Yitzchak interviewed them and asked:
--What kavanos do you have when you blow shofar?

Each one tried to impress R. Levi Yitzchak with special kavanos from the Ari and other great mekubalim. R. Levi Yitzchak was not impressed to engage any of them.

One day he was approached by a shofar blower who said:
--Rebbe, I am a plain Jew with four daughters to marry off and I do not have dowry for them. When I blow the shofar I think:
--Master of the universe, I did Your will and kept your mitzvos. So, You also, make my will Your will: Help me find husbands for my daughters.

R. Levi Yitzchak was overjoyed with this answer and said:
--Your kavanos are true kavanos. You shall be my ba’al toke’ah.