The whole book of Isaiah is loaded with valuable teaching on God's covenants with Israel. The New Covenant (spoken of explicitly in Jeremiah 31) is not mentioned in the book of Isaiah. Instead we get hints of it throughout the book. In Isaiah 54 there is an interesting look at the covenant that even ties into the ministry and word of Jesus Christ via quotation.

9 “For this is like the days of Noah to Me,
When I swore that the waters of Noah
Would not flood the earth again;
So I have sworn that I will not be angry with you
Nor will I rebuke you.
10 “For the mountains may be removed and the hills may shake,
But My lovingkindness will not be removed from you,
And My covenant of peace will not be shaken,”
Says the Lord who has compassion on you.

13 “All your sons will be taught of the Lord;
And the well-being of your sons will be great.
14 “In righteousness you will be established;
You will be far from oppression, for you will not fear;
And from terror, for it will not come near you. - Isaiah 54:9-10, 13-14 (NASB)

In the first two quoted verses the Lord lays down an interesting comparison. His judgment of the people of Israel, Hie desire to remove them from the land, is reminiscent of the flood with Noah. The people of Israel will not be removed from before Him again. His "covenant of peace" (Num 25:12; Eze 34:25; 37:26) will accomplish this. This is an unbreakable covenant and one that continues throughout generations. All of this motivates the comparison between this passage in Isaiah and the covenant described in Jeremiah 31 (31:35-37). The fruitfulness of the new covenant is that it will not be removed from the covenant people. Theologians are left with two interpretive options on who this covenant body then is. It is either the Jews (leading us to presume this passage hasn't been fulfilled entirely yet) or the church.

My opinion is that it belongs to the church. And that in the newness of the new covenant the church can remain convinced that God has not and never will break His covenant with us. We have been ensured that we will be presented as the bride for Jesus Christ (Eph 5; Rev 21).

The second portion of this quotation begins to describe some of the "fall out" of this covenant. In particular is Jesus' quotation of verse 13 in John 6:45. In the midst of a rather Calvinistic passage Jesus alludes to the manna of Israel (John 6:41, 49) and quotes Isaiah to prove his point. The NASB renders the passage "taught of God" while the ESV has chosen to render the passage "taught by God." The difference might be incredibly pertinent but the Hebrew does in fact support both. What is more interesting is the original verse Christ is quoting "All your sons will be taught of the Lord. And the well-being of your sons will be great."

God's new covenant, like His actions toward Noah, are for the well-being of the children of covenant members. Again, much like the passage in Jeremiah 31:35-37 there is a specific and tender focus on the offspring of these covenant members. Many ask how this covenant relationship and blessing works with the concept of predestination. That's part of the irony in Christ quoting this isn't it? He is looking at the Jews who are refusing to accept Him and He states clearly "you aren't the covenant people. For if you were you would have been taught of me."