A device for securing an element on a pipe, the device comprising: a compensating member made from elastic material, and two strands that each extend between a first end secured to the compensating member and a second free end; where the strands are able, by junction of the second ends, to form a strap provided to secure the element to the pipe. The compensating member is, on the one hand, stretchable when the device is tightened around the pipe and, on the other hand, gradually shrinkable over time to keep the strap taut when the pipe shrinks. The device may be incorporated in an assembly including an element provided to be secured to the pipe with the device. The assembly may be incorporated in an installation including a pipe. In addition, a method for implementing such a device.