I sent this question to a Catholic answers forum and thought I would pick the brains here as well. I meant to put this in the Religion forum... but didn't see a link for that when posting...
Pinging the finest Catholic minds I know of on this Forum...
There are more than seven.
The Phinehas Covenant or Priestly Covenant (Numbers 25):
7 When Phinehas son of Eleazar, the son of Aaron, the priest, saw this, he left the assembly, took a spear in his hand 8 and followed the Israelite into the tent. He drove the spear through both of them-through the Israelite and into the woman’s body. Then the plague against the Israelites was stopped; 9 but those who died in the plague numbered 24,000.
10 The LORD said to Moses, 11 “Phinehas son of Eleazar, the son of Aaron, the priest, has turned my anger away from the Israelites; for he was as zealous as I am for my honor among them, so that in my zeal I did not put an end to them. 12 Therefore tell him I am making my covenant of peace with him. 13 He and his descendants will have a covenant of a lasting priesthood, because he was zealous for the honor of his God and made atonement for the Israelites.” (Num.25:7-10).
From New Advent http://www.newadvent.org/cathen/01721a.htm
“THE ARK IN CATHOLIC TRADITION
Catholic tradition, led by the Fathers of the Church, has considered the Ark of the Covenant as one of the purest and richest symbols of the realities of the New Law. It signifies, in the first place, the Incarnate Word of God. “Christ himself”, says St. Thomas Aquinas, “was signified by the Ark. For in the same manner as the Ark was made of setim wood, so also was the body of Christ composed of the most pure human substance. The Ark was entirely overlaid with gold, because Christ was filled with wisdom and charity, which gold symbolizes. In the Ark there was a golden vase: this represents Jesus’ most holy soul containing the fulness of sanctity and the godhead, figured by the manna. There was also Aaron’s rod, to indicate the sacerdotal of Jesus Christ priest forever. Finally the stone tables of the Law were likewise contained in the Ark, to mean that Jesus Christ is the author of the Law”. To these point touched by the Angel of the Schools, it might be added that the Ascension of Christ to heaven after His victory over death and sin is figured by the coming up of the Ark to Sion. St. Bonaventure has also seen in the Ark a mystical representation of the Holy Eucharist. In like manner the Ark might be very well regarded as a mystical figure of the Blessed Virgin, called by the Church the “Ark of the Covenant” — Faederis Arca.
2. This list leaves out the clear covenantal language spoken to Isaac and Jacob. This was reflected in Leviticus 26:42 "And I will remember my covenant, that I made with Jacob, and Isaac, and Abraham. I will remember also the land:"
Why do we need another?
The people agreed to obey God! Remember, a covenant is an "agreement" between two parties ABOUT something. The proposal from God is likened unto a marriage covenant. God said,
"Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD" (Jeremiah 31:31, 32).
"For finding fault with them [there was no "fault" or flaw in the covenant itself—the fault was with the rebellious people!], he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Also look at the following list of "covenant" from crosswalk.com.
Ping to read later
Regardless of how many covenants there appears to be in Scripture, which will be determined by your own theological position, there is a tendency to try and think of the different covenants as being distinct and separate from each as each is unfolded in the biblical historical account. There are really only two covenants in Scripture. The covenant of works (Genesis 2:15) which implies “Do this (obey) and live” and the covenant of grace “Live and do this” which is seen in the proto euangelion statement of Genesis 3:15. Man failed to keep the covenant of works by his disobedience and so the covenant of grace is inaugurated in the Noahic covenant and unfolded throughout biblical history in the different administrations of the covenant of grace. Those of a dispensational theological position would call these the different dispensations of covenantal history and in a sense there are different dispensations, but a better way to understand it may be to refer to administrations of the covenant of grace. Each covenant declaration is an unfolding and expanding progression, pointing forward (through the prophets) to a future event that will be the culminative point in history which will dispense with the need for any more covenantal revelation. The incarnation of God the Son (His initial coming) is the fulfillment of the covenant of grace and the second coming of Christ is the consummation or full realization of that covenant.
This may be a rather simplistic explanation and there is much discussion on the subject about how we understand the different “Dispensations” or administrations of covenant theology. Suffice to say in conclusion.
Jesus Christ fulfills the demands of the covenant of works by his active obedience to the law as the second Adam in his sinless perfection, and his passive obedience to the penalty of the law as the propitiationary atonement for sin as the spotless Passover Lamb. All covenantal stipulations are fully met by him. Covenant rewards are won by him because of his obedience. Covenant curses are visited on him as the substitutionary atoning sacrifice in the place of covenant breakers. He is the great covenant keeper; in fact He is the only covenant keeper!
It sounds like the authors have been informed by modern pre-mil dispensationalism as taught in the “Bible Churches”.
From Wikipedia:
the most common list of dispensations is taken from the notes to the Scofield Bible:
* the dispensation of innocence (Gen 1:1–3:7), prior to Adam’s fall,
* of conscience (Gen 3:8–8:22), Adam to Noah,
* of government (Gen 9:1–11:32), Noah to Abraham,
* of patriarchal rule (Gen 12:1–Exod 19:25), Abraham to Moses,
* of the Mosaic Law (Exod 20:1–Acts 2:4), Moses to Christ,
* of grace (Acts 2:4–Rev 20:3 – except for Hyperdispensationalists), the current church age, and
* of a literal, earthly 1,000-year Millennial Kingdom that has yet to come but soon will (Rev 20:4–20:6).