Book of Hosea Chapter 3 Vs. 5

 Hosea Redeems His Wife

Afterward shall the children of Israel return, and seek the LORD their God, and David their king; and shall fear the LORD and his goodness in the latter days. Hos. 3:5

Afterward shall the... This part remains to be completely fulfilled. The part about returning is now in process of fulfillment, but seeking the Lord and David their king, and fearing God in the latter days remain to be fulfilled at the second coming of Christ (Zec. 12:10-13:1; 14:1-21; Mal. 4:5-6; Rom. 11:25-29; Rev. 11:1-2, 11:15; 20:4-10).

and seek the... This must refer to Messiah during the Millennium, as “in the last days” specifies (compare 55:3-4; Jer. 30:9; Eze. 34:23-24; 37:24-25). The Jews did not seek after Christ at His first advent. This reference has the Davidic Covenant as its background (2Sam. 7:12-17; Psm. Chapters 39 and 132).

David their king... David will be king over all Israel under the Messiah, but over the 12 apostles (Jer. 30:9; Eze. 34:23-24; 37:24).

the latter days... The tribulation period, Daniel's 70th week, etc.

David in the Kingdom: Although Christ will reign as sovereign in the kingdom; it is not clear whether He is the only One on the throne. Several passages suggest that David will reign in the Millennium under the Messiah (Isa. 55:3-4; Jer. 30:9; 33:15, 17, 20-21; Eze. 34:23-24; 37:24-25; Hos. 3:5; Amos 9:11).

These verses may be interpreted:

(1) Literally, with David being resurrected, returning to the throne, and have a sphere of regal authority under the regency of Christ.

One of Christ’s millennial titles, “King of kings, and Lord of lords” (Rev. 19:16), may suggest the presence of lesser kings and lords. So it will be that David will serve under Christ’s authority as vice-regent of Israel, just as others may similarly rule other regions or cities (Luke 19:12-18).

Those who suffer for Christ will someday reign with Him (2Sam. 7:12-16; Psm. 89:34-37; Eze. Chapter 47).

This is clearly slated to happen in the latter days. When they seek the LORD, they will find Him. Will find David, their king, reigning with the One they call Messiah, and we call Jesus. There will be a day of repentance. They are bought and paid for with that precious blood. We see in the following Scripture that God is God of all, not just a few.

1Tim. 4:10 "For therefore we both labor and suffer reproach, because we trust in the living God, who is the Savior of all men, specially of those that believe."

He provided salvation for everyone. Some will not accept that salvation. There is much controversy about these 10 tribes (Israel), and what happened to them. In the physical, they would be very hard to trace. In the spiritual sense, they are the lost world that comes to Christ, represented by the remnant consisting of all the tribes of Israel. Every person who ever lived, was a sinner, just like Israel before they came to Christ.

All Christians have been bought with the precious blood of Jesus, just like these of Israel were bought by God. Perhaps, this whole chapter has been speaking of all people who are away from God until Jesus came and set them free. It is God's goodness and mercy that saves us, not some act upon our part. We actually deserve to die for our sins. The wages of sin is death. Jesus marked our bill Paid in Full.

I will give a selection of Scriptures that help on this.

Rom. 11:26-27 "And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:" "For this [is] my covenant unto them, when I shall take away their sins."

Rom. 9:6-8 "Not as though the word of God hath taken none effect. For they [are] not all Israel, which are of Israel:" "Neither, because they are the seed of Abraham, [are they] all children: but, In Isaac shall thy seed be called." "That is, They which are the children of the flesh, these [are] not the children of God: but the children of the promise are counted for the seed."

Gal. 3:29 "And if ye [be] Christ's, then are ye Abraham's seed, and heirs according to the promise."

After Israel’s period of isolation she will repent and seek the Lord, rather than false gods (Hos. 2:7; 5:15; cf. Deut. 4:29). Israel will also recognize the authority of the Davidic monarchy, which it rejected at the time of Jeroboam I (cf. 1Kgs. 12:1-33). The nation will approach the Lord with a healthy sense of fear (trembling), even in the context of blessing. In the past the nation had taken the Lord’s gifts for granted and proudly turned away from His commandments (cf. Hos. 13:6; Deut. 8:10-18). The blessings (lit., “goodness”) in view here are wealth and agricultural bounty (cf. Deut. 6:11; Isa. 1:19; Jer. 2:7; 31:12, 31:14 where the same word, ṭûḇ, is employed). The concluding phrase, in the last days, was used by the eighth-century prophets as a technical expression for the time of Israel’s restoration predicted by Moses (Isa. 2:2; Mic. 4:1; cf. Deut. 4:30, “in later days”).