A consultant was an individual, who advised a person or an institution as an expert in a specific field.
Private investigators sometimes worked as consulting investigators assisting the police. William T. Riker called Sherlock Holmes "history's greatest consulting detective" in 2364. (TNG: "Lonely Among Us")
Shannon O'Donnel worked as a consultant engineer on the Millennium Gate in the early 21st century. (VOY: "11:59")
In 2370, Rom suggested himself to become Quark's consultant in negotiations with the Dosi. Quark agreed he needed help, but chose Pel instead of his brother. (DS9: "Rules of Acquisition")
In 2374, Morica Bilby was employed by the Tigan family as a favor to the Orion Syndicate, paid as a shipping consultant but without any actual work done, in order to provide for her and her children. (DS9: "Prodigal Daughter")
In 2375, Medical Consultant Program Beta one featuring a holographic Crell Moset was created to serve as a consultant for The Doctor. (VOY: "Nothing Human")