From the Zohar Chadash, Parshat Noach p. 22 (quoted from p. 67 in «the world of the Ger», by Chaim Clorfene with David Katz)

The Holy One, blessed be He, took Shem the son of Noah and made him the priest of God Most High to serve Him, and His Shechina rested upon him. And He called his name Melchizedek, King of Salem. And his brother, Japheth, learned Torah from him in his yeshiva. And then Abraham came along and taught Torah in the Yeshiva of Shem. And the Holy One, blessed be He, turned His attention to Abraham and forgot all the others. So Abraham prayed before the Holy One, blessed be He, that His Shechina should always dwell in the House of Shem, and He consented, as it says (Psalms 110:4), «You are a priest forever according to My word, Melchizedek.»

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Genesis 10:21,

And to Shem were also born [children; he was] the father of all the people of the other side [of the river], the brother of Japheth the elder.

Rashi, the father of all the people of the other side: of the river was Shem. See below 14:13. the brother of Japheth, the elder: I do not know [from the wording of the verse] whether Japheth is the elder or Shem. [The verse may be rendered: the elder brother of Japheth.] When Scripture says (11:10): “Shem was a hundred years old, etc.” two years after the Flood, you must say that Japheth was the elder, because Noah was five hundred years old when he first had children, and the Flood came to pass in the six hundredth year. Consequently, the eldest of his sons was a hundred years old [at the time of the Flood], and Shem did not reach [the age of] a hundred until two years after the Flood. — [from Gen. Rabbah 37:7] the brother of Japheth: But not the brother of Ham, for these two honored their father, and that one [Ham] disgraced him. [See Targum Jonathan, which renders: the brother of Japheth, who was great in the fear of the Lord. Perhaps this was Rashi’s source, but it is unlikely.]

 

Midrash Seder Eliyahu Rabbah ch. 24, says that Shem, the son of Noach, told the people, «You shall not kill, you shall not commit adultery, you shall not kidnap, you shall not bear false witness, and you shall not covet.»

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Genesis 14:18,

And Malchizedek the king of Salem brought out bread and wine, and he was a priest to the Most High God.

Rashi, And Malchizedek: The Midrash Aggadah (Targum Jonathan, Ned. 32b, Mid. Ps. 76:3) states that he was Shem, the son of Noah. bread and wine: This is done for those weary from battle, and he [Malchizedek] demonstrated that he bore no grudge against him [Abram] for slaying his sons (Tan. Lech Lecha 15). And according to the Midrash Aggadah (Gen. Rabbah 43:6), he hinted to him about the meal offerings and the libations, which his [Abraham’s] children would offer up there.

Genesis Rabbah 43:6, And Melchi Zedek [3]: This place [4] made its inhabitant righteous. [5] [Another interpretation] And the King of Zedek, [6] The Lord of Zedek (Josh. 10:1). [7] Jerusalem is called Zedek (righteousness), as it is written, Zedek (righteousness) lodged in her (Isaiah 1:21). King of Salem (Shelem). R. Isaac the Babylonian said: This implies that he was born circumcised. [8] Brought forth bread and wine. R. Samuel b. Nachman said: He instructed him in the laws of the priesthood, bread alluding to the shewbread, and wine to libations. [9] The Rabbis said: He revealed Torah to him, as it is written, Come, eat of my bread, and drink of the wine which I have mingled (Prov. 9:5). [10]

[3. Read as two words, as in the original.] [4. Sc. Jerusalem (Salem in the English).] [5. This is the comment on the word ‘Zedek’, which means righteousness.] [6. So translated now.] [7. E.V. ‘Adonis-zedek’.] [8. Translating Shalem whole, complete, i.e. the ‘whole’ king; cf. Gen. 17:1-10.] [9. Both were in charge of the priests.] [10. The speaker is Wisdom personified (v.1-3); hence, ‘bread‘ and ‘wine‘ there refers to the Torah.]

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Leviticus 26:45,

But for their sakes I will remember the Covenant of the Ancients, for which I brought them out of the land of Egypt in the sight of the nations, that I might be their God; I am the Lord.

Covenant of the Ancients: Adam, Seth, Noah, and Shem (Midrash Rabba on Leviticus 26:45)

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