Daniel 10:14 says "Now I am come to make thee understand what shall befall thy people in the latter days: for yet the vision is for many days." The angel sent from God to give Daniel the prophecies in Daniel 11 and 12 tells Daniel that he, the angel, was sent to make Daniel understand what was to happen to his people in the latter days, and that this vision is for many days.
The Pharisees of Christ's time would have insisted that "thy people" must be Old Covenant Israel, the people of Judaism of the period of time in which the Pharisees led Old Covenant Israel. However, several of the Old Testament prophets were given some information on the remaking of Old Covenant Israel, especially the writer of II Kings (II Kings 21: 13), Isaiah in Isaiah 29: 16, Jeremiah in Jeremiah 18: 1-6, Hosea in Hosea 2: 23 and Haggai in Haggai 2: 9. Why would not Daniel also have some knowledge, though seen through a glass darkly, of the remaking of his people Old Covenant Israel? Even if Daniel was not given specific information on that remaking of Israel to come we can, by use of Isaiah 28: 10 -"For precept must be upon precept, precept upon precept; line upon line, line upon line; here a little, and there a little -" use these other Old Testament prophets to interpret who "thy people" are in the latter days where this vision is for many days. Daniel's people in the Christian era after the Cross are Israel remade in Jesus Christ.
Christ warned of the leaven of the Pharisees in Matthew 16: 6, and in Matthew 16: 12 he explained that the leaven of the Pharisees - and of the Sadducees -was their doctrine. The leaven of the Pharisees - their doctrine - is made manifest in the Little Horn of Daniel 7: 8, 20-21. The Little Horn of Daniel 7: 8, 20-21 is the same as one of the heads of the first beast whose deadly wound was healed in Revelation 13: 3-5. Note that in Daniel 7:8 the Little Horn has a mouth speaking great things, and in Revelation 13: 5 the head on the first beast whose deadly wound was healed has a mouth speaking great things.
The leaven of the Pharisees would lead to the view that "thy people" of Daniel 10: 13 must be Old Covenant Israel and cannot be any other. The leaven of the Pharisees in the timeline of Christians would also lead to supporting the doctrine that the Old Covenant people of God, by their physical bloodline, still exist as the chosen people.
Israel reborn in Christ (John 3: 1-6) took on the role of Israel shining the light of God into those not of the Old Covenant bloodline. Christ the hope of glory - Christ in you (Colossians 2: 27) - comes into them. Israel remade as a spiritual house (Jeremiah 18: 4, I Peter 2: 5,9) took on, in the era of the New Covenant, the role of Israel shining the light to those not of the bloodline (Isaiah 42: 6).
Hosea 2: 23 says "...I will say to them which were not my people, Thou art my people: and they shall say, Thou art my God."
Hebrews 10: 9: "He taketh away the first, that he may establish the second." In remaking Old Covenant Israel, to fulfill Jeremiah 18: 1-6 - as well as II Kings 21: 13 and Isaiah 29: 16 - Christ took away the Old Covenant that he could establish the New Covenant.
Then, in Haggai 2: 9 that prophet states that "The glory of this latter house shall be greater than that of the former, saith the Lord of hosts..." The latter house is seen in Jeremiah 31: 31-33, on the New Covenant, but here Jeremiah does not explain what changes are to be made as God is to remake Old Covenant Israel, except that in the New Covenant God will put his law in their inward parts and write it in their hearts. Christ in John 3; 1-6 tells Nicodemus, a Pharisee, that in order to get into the kingdom of God anyone must be born again. Paul explains what being born again involves, and Christ in you is a big part of that transformation.
“I the Lord have called thee in righteousness, and will hold thine hand, and will keep thee, and give thee for a covenant of the people, for a light of the Gentiles” (Isaiah 42:6).
Paul explains a part of this remaking of Old Covenant Israel to the Romans
“Behold, thou art called a Jew, and restest in the (Old Covenant) law…And art confident that thou thyself art a guide of the blind, a light of them which are in darkness…but the name of God is blasphemed among the Gentiles through you.....For he is not a Jew, which is one outwardly...which is outward in the flesh. But he is a Jew which is one inwardly....in the spirit, and not in the letter; whose praise is not of men, but of God." (Romans 2:17, 19, 24, 28-29).
In the book of the Acts Paul states that God has revealed that under the New Covenant, the born again body of Christ fulfills the prophecy in which Israel is the light to the Gentiles:
“For so hath the Lord commanded us, saying, I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth. And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed." (Acts 13:47-48).