The phrase "run contraband" refers to the act of smuggling prohibited items or materials. To describe this activity in a different way, one could use synonyms such as traffic illicit goods, transport forbidden items, or clandestinely move contraband. Other possible synonyms might include surreptitiously distribute prohibited materials, covertly convey banned materials, or underhandedly transfer contraband. Regardless of the specific term used, the meaning behind the phrase "run contraband" remains the same: an illegal act of transporting items that are not permitted to cross certain borders or boundaries.