In a flashback sequence, it's revealed that Gaspar was transported from 12,000 B.C. to the End of Time due to Lavos' power.
After Crono's death and Magus joins the party, they travel to the End of Time seeking Gaspar's advice. He gives them the "Chrono Trigger", a magical egg with the power to bring the dead back to life. He says to find Belthasar because he knows how to use it.