I came across this article from which I would like to quote something:
The concept of Malchuso b'khal adaso allows Bnei Yisroel to transform the teruah from a destructive sound of war into a sound that shows the friendship and love between HaKadosh Baruch Hu and Knesses Yisroel. The root of the word "רעה" means "friend", as Elokim horoeh osi me'odi, G-d who has been my shepherd (Breishis 48:15, see the Ramban ad loc.). This, indeed, is the teruah of "u'teruas Melech bo, the blast for the King is among them" (Bamidbar 23:21) mentioned in the verses of the Malhiyos blessing. This connotes closeness and intimacy between Ribbono Shel Olam and Bnei Yisroel and is proof that we are priviledged to have HaKadosh Baruch Hu as a friend. This is not din but rather rachamim, mercy.
With this new given meaning of teruah: "teruah" denotes a sense of kinship and closeness. Bamidbar 23:21 “He perceived no iniquity in Jacob, and saw no perversity in Israel. Hashem his God is with him, u’teru’at Melech bo” (Bamidbar 23:21). Rashi renders this last phrase as “and the friendship of the King is in him,” since, he explains, the word teru’ah is a derivative of the Hebrew word re’ut, friendship.
Is this what 'the shout of a King amongst them' or 'shouting for the King is among them' or 'And their King’s acclaim in their midst' means? Why is this friendship or closeness specifically connected with the sound of a Shofar in the form of a Teruah blast?
I didn't understand these explanations quite well, so maybe someone could explain it more clearly to me.