Psst… There is a hidden market for six-figure jobs. Here’s how to enter.

Almost every day, someone quietly looking for a key to rent calls Diane Hessan ask the same question: Who do you recommend?

Ms. Hessan, a former CEO of a consulting group who sits on the boards of Panera Bread, Eastern Bank and Tufts University, is one of Boston’s best-connected business figures – and something of a word keeper of going into a speakeasy for a six-figure job searcher.