Translation
To that same degree He has become the guarantor of a better covenant.
Paraphrase
to that same degree Jesus has become the enabler of a better covenant.
Because He Is Alive, Jesus Is also a Guarantor of the New Covenant
The degree to which Jesus is a better High Priest, whose priestly office is based on a better foundation, is the degree to which He is able to be the guarantor of a better covenant, one which was inaugurated with better assurance – His own blood.
Jesus is the mediator of the New Covenant, the sacrifice of the New Covenant, and a witness of the New Covenant in that He is the guarantor of the same. Thus the Holy Spirit and Jesus are both guarantors of this covenant under which we live. They both provide assurance that God will do what He said He would do. They also enable us to live for God’s glory. The Holy Spirit enables us by applying to our lives the full provision of everything we need for life and godliness (II Pet 1:3). Jesus enables us by interceding to God the Father on our behalf (Heb 7:25). Whereas Satan accuses us before God (Rev 12:10), the Holy Spirit and Jesus both intercede on our behalf (Rom 8:26 & Heb 7:25).