Did Cleopatra have a leopard?

Yes, leopards were tamed back than, though it did eat her sisters pet monkey!

It's name was Arrow.
It's highly unlikely. Oh, yes, it makes a nice story book scene with the exotic queen or princess having an exotic pet. But in reality a leopard in ancient times, just as in present times, was a wild animal, unpredictable and impossible to train to use a litter box. Its doubtful that there would be one slouching around the royal palace. Don't even think about what would happen if the leopard got hungry.