There is and should be a relationship between Old Testament laws and modern laws. We may no longer be subject to Old Testament ceremonial law, but that does not invalidate God's moral principles set down in the Old Testament. Murder is still wrong. Thus, since murder is wrong, the penalty for murder must still be implemented. Second, even if we accept the premise that the Old Testament law code was specifically and uniquely for the Old Testament theocracy, this still does not abolish the death penalty.
Capital punishment is to be implemented because of the sanctity of human life.
We are created in God's image. When a murder occurs, the murderer must be put to death. This is a universally binding principle not confined merely to the Old Testament theocracy. Third, it is not just the Old Testament that teaches capital punishment. Human governments are given the responsibility to punish wrongdoers, and this includes murderers who are to be given the death penalty.