Dragon, along with Snap, were the dragon like henchmen of Hecuba. When Hecuba captured the Second Doctor, Jamie McCrimmon and Zoe Heriot in her domain, Snap and Dragon served dinner courses to Hecuba and the Doctor.
When Hecuba finally trapped the Doctor in her time booth, the Doctor told Hecuba that the TARDIS was indestructible (which was false). When Hecuba tried to destroy the TARDIS, it jammed time in her domain. Jamie and Zoe then freed the Doctor and moved the frozen Hecuba, Snap and Dragon into the time booth and set up a time loop. When time resumed, Dragon, along with Snap and Hecuba, were trapped with Marie Antoinette for the rest of time. (AUDIO: The Queen of Time)