First, God applies a spiritual interpretation to these words that He inspired His prophet Hosea to write, indicating to us that the prophecy is ultimately fulfilled by the Gentiles coming into Christ along with the remnant of Jews. In this prophecy in Hosea (and others like it in the OT), Judah (the southern kingdom) is used spiritually to refer to the remnant of God's people from the nation of Israel, and Israel (the northern kingdom) is used spiritually to refer to the remnant of God's people from all of the Gentile nations. You have to understand that God does everything for a reason! There is nothing arbitrary or insignificant about His inspired word or His providential control of history.
When He split the kingdom in two, He began to use this event to speak symbolically about the two groups of people that He has in this world, those from the Jewish nation, and those from the Gentile nations. This is what the kingdoms of Judah and Israel symbolized - the Jews and the Gentiles! The language that we see in the OT about re-gathering the dispersed of the northern kingdom of Israel ultimately has its fulfillment in the NT church age with the remnant of the Gentile nations being brought into the body of Christ along with the remnant of the Jewish nation to form the Church. God's people are now one, with one shepherd and King over them, the Lord Jesus Christ (referred to as "David their king" in Hosea 3:5). Ezekiel speaks of the exact same idea when he prophecies of the joining of the two sticks.
Ezekiel 37
16 Moreover, thou son of man, take thee one stick, and write upon it, For Judah, and for the children of Israel his companions: then take another stick, and write upon it, For Joseph, the stick of Ephraim and for all the house of Israel his companions:
17 And join them one to another into one stick; and they shall become one in thine hand.
Ezekiel 37
20 And the sticks whereon thou writest shall be in thine hand before their eyes.
21 And say unto them, Thus saith the Lord GOD; Behold, I will take the children of Israel from among the heathen, whither they be gone, and will gather them on every side, and bring them into their own land:
22 And I will make them one nation in the land upon the mountains of Israel; and one king shall be king to them all: and they shall be no more two nations, neither shall they be divided into two kingdoms any more at all.
23 Neither shall they defile themselves any more with their idols, nor with their detestable things, nor with any of their transgressions: but I will save them out of all their dwellingplaces, wherein they have sinned, and will cleanse them: so shall they be my people, and I will be their God.
24 And David my servant shall be king over them; and they all shall have one shepherd: they shall also walk in my judgments, and observe my statutes, and do them.
And once more, Jesus Christ Himself assusres us of the spiritual fulfillment of the prophecy:
John 10
14 I am the good shepherd, and know my sheep, and am known of mine.
15 As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep.
16 And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd.
Here is the fulfillment of the prophecy - one fold (Jew and Gentile together) with one shepherd over them, "David their king" is the Lord Jesus Christ Himself! The time period in view is the NT church age, after the crucifixion of Christ, which made possible the outpouring of the Holy Spirit, bringing peace (of Salvation), cleansing from sin and iniquity, and restoration to the Israel of God, all those chosen from the foundation of the world (BOTH Jew and Gentile alike). I hope you can see that all of the prophecies that we have looked at so far were fulfilled in Jesus Christ at the cross, and in the outpouring of the Holy Spirit that followed.
This is why we read in Zechariah 14:8 refers to the former sea and the hinder sea. It is a reference to the Jews (former sea) and Gentiles (hinder sea) who were both cleansed and brought to life by the Holy Spirit, forming one, unified Israel of God - the body of Christ. This is the restoration of Israel! This has absolutely nothing to do with that nation in the Middle East which has been in continuous rebellion against God for the last 2000 years. It has everything to do with the fulfilling of God's promise to Abraham that all nations of the earth would be blessed through his seed (Jesus Christ) - the promise of the Holy Spirit!
Let them with spiritual ears let him hear!