Immediately after the flood, God did not establish a covenant specifically with Shem (even though Abraham was a descendant of Shem (Genesis 11:26) and Jesus was born through the line of Abraham (Matthew 1:1)). But God made a covenant with Noah and all his descendants.
Yes, there is a foreshadowing of Jesus in this covenant, which is recorded in Genesis 9.
Here is a summary of the main points of this covenant:
God wanted Noah’s descendants to repopulate the world. The Lord said, “Be fruitful and multiply, and fill the earth.” (Genesis 9:1)
God gave Noah’s descendants animals to eat besides plants. So people started to consume meat whereas previously they only ate vegetables. The Lord said, “Every moving thing that is alive shall be food for you; I give all to you, as I gave the green plant.” (Genesis 9:3)
God forbade the eating of blood and the shedding of human blood by murder. “Only you shall not eat flesh with its life, that is, its blood. Surely I will require your lifeblood; from every beast I will require it. And from every man, from every man’s brother I will require the life of man.” (Genesis 9:4-5)
God established the covenant of the rainbow with Noah, his descendants, and every creature that came out of the ark. “It shall come about, when I bring a cloud over the earth, that the bow will be seen in the cloud, and I will remember My covenant, which is between Me and you and every living creature of all flesh; and never again shall the water become a flood to destroy all flesh.” (Genesis 9:14-15)
The covenant of the rainbow is significant because people and animals might have developed a fear for rain if God hadn’t established this covenant. Every time it rained, people might think that life is over and a flood will wipe them out again. But God promised He will never destroy the earth again by flood. And His promise of peace is in the rainbow.
It is interesting how the rainbow looks like a bridge. In a way, God establishes a bridge between God and humans. This foreshadows the bridge of peace we have through Jesus.
Jesus referred to Noah when He talked about His second coming, “For the coming of the Son of Man will be just like the days of Noah. For as in those days before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noah entered the ark, and they did not understand until the flood came and took them all away; so will the coming of the Son of Man be.” (Matthew 24:37-39)
Noah spent many days building the ark. And after he and his family entered the ark, seven more days passed (Genesis 7:4). There was enough time for other people to enter the ark also if they believed in what God said and repented.
However, none of the others entered because they were too caught up in worldly affairs.
God always provides a way to save us. He saved Noah and his family from judgment through the ark. Now God saves us from judgment through Jesus Christ. If we believe in Jesus who paid the price for our sins and repent, we will be saved.
In Jesus, we have true peace with God. And Jesus is the bridge to God the Father.
Jesus said: “I am the way, and the truth, and the life; no one comes to the Father but through Me.” (John 14:6)
Let us not love the world and miss true salvation.