Duct tape was a type of multipurpose adhesive tape used on Earth.
In 1996, a homeless and marooned Captain Braxton duct taped a cardboard sign to a lamp post. (VOY: "Future's End")
In 2154, Hoshi Sato, envious of Trip Tucker's engineering skills, commented on how she wished she could "fix warp engines with duct tape and a pocket knife." He responded, stating that "it's a bit more complicated than that." (ENT: "Observer Effect")
In 2257, Jett Reno told Paul Stamets that she could fix almost anything with duct tape. (DIS: "An Obol for Charon")