Joseph Fielding Smith (Quorum of the Twelve)

What is the new and everlasting covenant? I regret to say that there are some members of the Church who are misled and misinformed in regard to what the new and everlasting covenant really is. The new and everlasting covenant is the sum total of all gospel covenants and obligations. (Doctrines of Salvation, 1:156)

Now there is a clear-cut definition in detail of the new and everlasting covenant. It is everything—the fulness of the gospel. So marriage properly performed, baptism, ordination to the priesthood, everything else—every contract, every obligation, every performance that pertains to the gospel of Jesus Christ, which is sealed by the Holy Spirit of promise according to his law here given, is a part of the new and everlasting covenant. (Doctrines of Salvation, 1:158)

Bruce R. McConkie (Quorum of the Twelve)

"The new and everlasting covenant" is the fulness of the gospel, and the gospel is the covenant of salvation that the Lord makes with men. It is new because it has been revealed anew in our day; it is everlasting because it has always been had by faithful people, not only on this earth but on all the earths inhabited by the children of our Father. (Brigham Young University, 6 November 1977)

D. Todd Christofferson (Quorum of the Twelve)

The scriptures speak of the new and everlasting covenant. The new and everlasting covenant is the gospel of Jesus Christ. In other words, the doctrines and commandments of the gospel constitute the substance of an everlasting covenant between God and man that is newly restored in each dispensation. If we were to state the new and everlasting covenant in one sentence it would be this: "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life" (John 3:16).

Jesus explained what it means to believe in Him: "Now this is the commandment [or in other words, this is the covenant]: Repent, all ye ends of the earth, and come unto me and be baptized in my name, that ye may be sanctified by the reception of the Holy Ghost, that ye may stand spotless before me at the last day" (3 Nephi 27:20). (Ensign, May 2009)