As its name suggests, it looks like a wyvern (a type of dragon from European mythology), red in color. Its upper limbs have a pair of large wings and two vertical horns on its head.
Later, this wyvern is seen when Esdeath was patrolling in search of Modified Hazardous Beast. When her teacher sees what appears to be one (which would later turn out to be Tatsumi), she falls off her saddle and leaves her to her fate.
Some Imperial soldiers also have some of these trained creatures. Two of them saw themselves riding wyverns when they went to announce Esdeath to return to the Capital after his campaign against the western kingdoms.