Jessie will ask Jade to capture, preferably alive, an imperial Magitek Knight or Illusionist. Magitek Knight and Illusionists are recently created, or at least re-discovered, Jobs. It should be impossible for soldiers native to Crystallis to already have them, so she'd need to study them to see what the Empire has done exactly to make this possible.

Given he is in the military, she has good hope he'll be able to encounter one during a mission. Upon bringing her one such soldier either dead or still alive, Jessie will give him the White Mage Job.

You can chose to handwave this quest or log it with other players, at your convenience.