Bestiarius or Venator (Gladiator Ranger)
by Marc Saindonin the late roman empire, "hunts" were probably more popular as entertainment than gladiator matches, so if Thyatis follows similar fashions, the Ranger might actually be a suitable class to deal with the various exotic animals, as caretakers, trainers or those that put them down.
Also, female gladiators were a thing.
Gladiatrix
Bestiarius
Venator
Venatio
