The term 'Do Gumshee Work' is a reference to the job of a private detective, also known as a gumshoe. A gumshoe is someone who investigates and gathers evidence for criminal cases. The crossword solution for this term is 'TRAIL', which refers to the process of following clues and leads in order to uncover information. This is an important part of the gumshoe's job, as they must be able to track down suspects and witnesses in order to build a case.