The Dragon Soul vanished after the ancient war, and it was stolen by Malfurion.
The official Warcraft novels were not very detailed in their description of this plot, and due to repeatedly poring over the texts, it was impossible to determine exactly what had happened at the time; currently, there are two rather vague theories.
After the ancient war, the Dragon Soul fell into the hands of the Guardian Giant Dragons and the Night Elves, but the Guardian Giant Dragons would feel weak and powerless as they approached the Dragon Soul, so they entrusted Malfurion with its safekeeping.
Malfurion hid it away.
However, during the Second Orc War that came later, Deathwing used the Dragonmaw clan to find the Dragon Soul, and with it, he enslaved Alexstrasza, the Red Dragon queen.
But exactly how this all happened was not explained in detail.
Could it be that Deathwing was coming for the Dragon Soul? And the Dragon Soul was still in the hands of the Night Elves? Yes, that must be it.