What is meant by covenants that are made at "other times"? President Brigham Young answered this question when he said that there are additional ordinances that will be given to the faithful in the next life:
We will operate here, in all the ordinances of the house of God which pertain to this side the veil, and those who pass beyond and secure to themselves a resurrection pertaining to the lives will go on and receive more and more, and will receive one after another until they are crowned Gods, even the sons of God.By means of the New and Everlasting Covenant, our Father in Heaven helps His children increase in spiritual stature. Although at baptism we execute our first gospel covenant in mortality by "relying wholly upon the merits" of Christ, the Lord intends that we gradually gain spiritual strength through making and keeping additional covenants until, someday, we come to the point where "we shall be like him." As Chauncey Riddle has written:
... [Human] beings may be saved only by binding themselves to Christ. It is as if our task were to stand straight and tall before Father, but because of the Fall, we are broken and twisted. The Savior is our straight and tall splint. If we bind ourselves to Him, wrap strong covenants around us and Him that progressively draw us up into His form and nature, then we can become righteous as He is and can be saved. But without Him we are nothing.... The New and Everlasting Covenant is our detour whereby our Savior strengthens us until we can tread the narrow way of justice and mercy on our own....