Before we recite the Thirteen Middos haRachamim, there is an introductory paragraph about how Hashem revealed them to Moshe Rabbeinu when the latter was praying for the nation to be forgiven after the Cheit haEigil. It is used all but the first time the Middos are recited every Selichos service and begins:

קֵל מֶלֶךְ יוֹשֵׁב עַל כִּסֵּא רַחֲמִים
מִתְנַהֵג בַּחֲסִידוּת.
מוֹחֵל עֲווֹנוֹת עַמּוֹ,
מַעֲבִיר רִאשׁוֹן רִאשׁוֹן.
מַרְבֶּה מְחִילָה לְחַטָּאִים,
וּסְלִיחָ לַפּוֹשְׁעִים.

G-d, King, Who sits on the Throne of Compassion
Who conducts Himself with Lovingkindness
Who forgives the sins of His nation
He removes them – first one first
Increasing Forgiveness to sinners
and pardons to transgressors. 

Accepting Hashem as our King is perhaps the central theme of Rosh haShanah. What does it mean, though, to accept a King?

I want to contrast two terms: Melekh and Mosheil. The rabbinic idiom is “ein melekh belo am – there can be no king without a nation.” A melekh has a covenant with his people. The work together to supply the resources the country needs, and to build it into something better than it was.

In contrast a mosheil, who rules whether or not the citizenry cooperate, will at times be force to put them in their place. A citizenry who didn’t sign on will at times do things that aren’t for the country’s good, or even in their own best interest.

Hashem as Melekh can “Sit” on the Throne of Rachamim because doing what is best for us wouldn’t require discipline to impose His Will.

To accept Hashem as King is to sign onto that covenant. To willingly have Him rule you. And the more we succeed in doing so, the more Rachamim and less Din will reach us.

As we say in Ashrei (Tehillim 145:13):

מַֽלְכוּתְךָ֗ מַלְכ֥וּת כׇּל־עֹֽלָמִ֑ים
וּ֝מֶֽמְשֶׁלְתְּךָ֗ בְּכׇל־דֹּ֥ור וָדֹֽור׃

Your Kingship is for all of time;
Your Rule is for all generations.

While “for all generations” is certainly a long time, it sounds limited compared to “all of time”. Hashem is only Moshel during the course of History. In the messianic era, He will be Melekh.

As we say after Aleinu (Zekhariah 14:9)

וְהָיָ֧ה יְהֹוָ֛ה לְמֶ֖לֶךְ עַל־כׇּל־הָאָ֑רֶץ
בַּיּ֣וֹם הַה֗וּא יִהְיֶ֧ה יְהֹוָ֛ה אֶחָ֖ד וּשְׁמ֥וֹ אֶחָֽד׃

Hashem will be Melekh over the whole world;
in that day Hashem will be One, and His Name (i.e. how people think of Him) will be one.

A very short second thought:

Did you wonder what “מַעֲבִיר רִאשׁוֹן רִאשׁוֹן – He removes them (i.e. the sins) – first one first” means?

Here is how I relate to it.

Ever have a fight with your wife or husband, and every incident that seems to be related to the same character flaw comes up? So that instead of just arguing of what happened right now, you’re arguing over things done in the beginning of your marriage too?

Not that.