A tensioning device for a compensating sheave. The compensating sheave is provided with a housing. The tensioning device comprises: a first snap-fit member; a second snap-fit member; and a trigger mechanism comprising a resilient assembly and a limiting assembly, wherein the limiting assembly is provided with a limiting member, wherein the tensioning device has a first state in which the limiting member abuts against a second end of the first snap-fit member so that a certain clearance is kept between a first end of the first snap-fit member and the second snap-fit member and a second state in which the limiting assembly is moved downward so that the first end of the first snap-fit member is rotated downward until the first end is snap-fitted with the second snap-fit member. A compensating sheave is provided with the above-described tensioning device and an elevator is configured with the above-described compensating sheave.
