So there really isn’t much development of the thought of eternal life in the Old Testament. There is the very well developed concept of God’s blessings that extend beyond this life through the birth of children, actually specifically sons. This Psalm perfectly reflects that well developed concept which we find in the Old Testament. Verse 6 really shows that this is what we all want, isn’t it? Don’t we all want to see our children’s children and have peace in the land in which we live? I would say we do.
But as Christians we know that life consists more than how many children we end up producing and how many children our children end up producing. While it is a great goal toward which to look, we know that the eternal life which is promised of us also entails an eternal life where we are present both bodily and spiritually once we die on this earth. This is what we look forward to more than anything else.