I just completed preparation of a bible class on the book of Malachi which I am currently teaching to my men's group. So your question has perfect timing.
The covenant with Levi is just a reference to the covenant of the law which God made with Moses and the Israelites. If you look at the next few verses, we see that the description sounds exactly like Jesus; ie, My covenant was with Him for life and peace, He respected God, the law of truth in His mouth and iniquity was not found on His lips and He did turn many away from iniquity; the priest's lips should keep knowledge because He is the Lord's messenger.
The "messenger" shows up again in Chapter 3 with the prophesy of the Messiah.
The Book of Malachi is the perfect book to conclude the Old Testament. God states that Israel has not kept the law from the time that He gave it to Moses (Chapter 3:7). God is so disgusted by Israel's lack of regard for the Lord and His commands (especially their offerings of diseased and lame sacrifices) that He states that He will no longer accept any more sacrifices from them (Chapter 1:11). God is in effect shutting down the covenant of the Law, again perfect contextual sense since this is the last written communication of the OT.
God then states that only the coming of Messiah will "fix" the relationship with God and only then will sacrifices (now in New Testament context) will be acceptable (Chapter 3:3).
God then tells Israel to retun to Him. This "return" is the same "return" spoken of in Deuteronomy Chapter 30, where God tells Israel that He will "return" Israel to Him and He will circumcise their heart. According to Dr. Charles P. Bayliss of Dallas Theological, this is a unilateral action by God and which refers back to the promise that God made to Abraham, ie I will bless you just because I love you. No action was required on Abraham's part, he just believed God and God accounted that as righteousness.
The "return" (which is the actual definition of biblical repentance) is highlighted in the persons of Elijah and John the Baptist. Elijah was the prophet in 1 Kings 18 that "returned" the heart of Israel after the incident with the 450 prophets of Baal. In verse 37, right before God send the fire down from heaven, Elijah says, "Hear me, O LORD, hear me, that this people may know that thou art the LORD God, and that thou hast turned (returned) their heart back again."
This is the same "return" that Jesus and John the Baptist were speaking about, ie return to the promise of Abraham; leave the covenant of the Law and return to the covenant of the promise. For God always intended that salvation would be by His grace and NEVER by the efforts of man.
This "return" is exemplified in the book of Acts where the Jews were told by Peter to "repent and return", while the Gentiles were never told this but only to believe in Jesus for the Gentiles had nothing to "return" to. That is, they never had the law from which to return to the promise.
So as you can see, the Book of Malachi is tremendously fascinating and so much more than a few verses that promise material prosperity if you just tithe properly. When you study the book for yourself, you will see that those tithing verses in Chapter 3 are not a promise by God of material blessing but a scathing reminder of Israel's failure to keep the whole law as they are a reference back to Deuteronomy 26-30 which outlines the blessing and the curse. God bless.