"Diplo-in-training" means that the author buys into the widely held notion that Chelsea is in the consulting business because many consultants from her firm wind up becoming bigshot lobbyists and/or diplomats.
Ahhh... thank you for clearing that up.
Now that I know what they mean it's clear why I didn't know what they meant in the first place. (people and places I will never come across in my life) ;-)