'Covenant' in the Bible

He has qualified us [making us sufficient] as ministers of a new covenant [of salvation through Christ], not of the letter [of a written code] but of the Spirit; for the letter [of the Law] kills [by revealing sin and demanding obedience], but the Spirit gives life.

But [in fact] their minds were hardened [for they had lost the ability to understand]; for until this very day at the reading of the old covenant the same veil remains unlifted, because it is removed [only] in Christ.