I think it may be helpful to look in a bit more depth at the 'Old Covenant'.
The Sinaitic covenant is the first of two covenants made with a people through a mediator. It was made with the Israelites at Sinai through Moses, so it is not quite accurate to call it the Mosaic covenant because it was not made with Moses. It is commonly referred to as the ‘Old Covenant,’ though in fact it is only called that once in the Bible, in 2 Corinthians 3:14. The writer to the Hebrews refers to it repeatedly as the First Covenant, which is most significant because it suggests that God views it as something different to those covenants that went before it.
I think what most overlook is that the "first" and "second" or "old" and "new" are VISIBLE PUBLIC HUMAN ADMINISTRATIONS of these covenants whereas the former covenant or covenants of promise are purely divine administrations. Hebrews 9:1 makes this abundantly clear. The "old" and "new" have a very public visible human administrative aspect. Both have a specific point of origin in time. Both have public qualified ordinances. Both were sanctified by shedding of blood. Both have pubic qualified ministries, mission and scriptures pertaining to each and both are limited in their future extent. The Old continued to what it anticipated was fulfilled - Christ on the cross. The New continues to the "end of the age" (Mt. 28:19-20).
Certainly the "new" is better than the "old" in many ways as a visible public human administration. However, neither is the completion or fulfillment of the "everlasting covenant" as that covenant is not completed until what we see in Genesis 1:26 as a sinless new world is recovered once again in another sinless new world (Rev. 21-22:4).
Now Roman Catholicism sees the obvious visible human administrative element in these two covenants and claims to be the visible administrator in an effectual and legislative sense. Therefore they claim that salvation is actually obtained and applied by the church and through its administration of the ordinance just as it was through the levitical administration under the old covenant.
However, there is no actual literal visible administration of salvation under either covenant by the human administration involved. The institutional and public human administration in both covenants is confined to declarative and ceremonial in both covenants. In both covenants the actual administration of salvation is totally by divine administration according to the "blood of the everlasting covenant" or the Trinue administration of salvation directly to God's elect under both covenants.
Here is the issue that most fail to deal with. Both covenants have an authorized visible human administration (Heb. 9:1). Both have public houses of worship. Both have a qualified public ministry. Both have scriptures. Both have public qualified ordinances. Both have a qualified commission. Both have a public immersion in the Spirit. Both have chosen prophets in their point of origin (Moses, Christ).
The problem is to distinguish between what function the human administration plays in these covenant administrations versus what function God serves through these administrations.
In the former, the human administrative function was not designed to obtain life (Gal. 3:21) but to serve as a school master to educate the individual Jew with regard to the nature of sin and then lead them to faith in the gospel of Christ as expressed in the sacrificial ceremonial types. The actual fulfillment of both purpose within the individual's heart (recognition of sin and recognition of Christ and coming to him by faith) was purely due to the divine administration of the "everlasting covenant."
In the new, the human administrative function is purely declarative. The ordinances are ceremonial or pictorial, based upon a much clearer presentation of the gospel of the "everlasting covenant" because of the fulfillment at Calvary and the empty grave accompanied with apostolic scriptures.
I am afraid that most commentators ignore the human adminstrative aspect of each covenant administration because they are not able to separate it from the divine administrative aspect or in reaction to Roman Catholicism.
However, those of us who have a proper understanding of the true nature of the New Testament church and its ordinances, ministry and mission need not fear or fail to properly dissect the human from the divine adminstration aspects in each covenant.
The "everlasting covenant" is all about the ultimate restoral of paradise lost. What God began in Eden is finished in the New heaven and earth. The covenants of "promise" are progressive manifestations of that everlasting covenant along with progressive revelations of the gospel promise in "seed" form first given in Gen. 3:15. The "old" or "first" covenant as a HUMAN ADMINISTRATION is instructive and declarative in nature while actual literal individual salvation is wholly by the divine administration of the everlasting covenant. The same is true to the "second" or "new" covenant as a HUMAN ADMINISTRATION except what the first anticipates the second declares to be fulfilled. The second is the superior covenant, not because salvation is secured by the human administrative aspect, any more than under the former covenant, but because this covenant administration's declarative function stands on the fulfillment of the promised seed and anticipates the coming prophetic fulfillment of the "everlasting covenant" in a new heaven and earth, thus restoring paradise lost.