(source: https://www.rsc.org/periodic-table/element/66/dysprosium)

The main use of dysprosium is in alloys for neodymium-based magnets. This is because it is resistant to demagnetisation at high temperatures: Permanent Magnet Alloy For Elevated Temperature Applications (1988). This property is important for magnets used in wind turbines (Mixed Rare-Earth Based High-Coercivity Permanent Magnet (2007)), and electrical vehicles (Method For Manufacturing Permanent Magnet That Is Used In Electric Traction Motor Of E.G. Hybrid Vehicle, Involves Sintering Preset Shape Such That Magnet Is Formed With Uneven Distribution Of One Of Materials On Surface Of Other Material (2013)). 

Dysprosium-doped alkaline earth materials are used in lasers: Alkaline Earth Halide Divalent Dysprosium Laser Materials (1966).

Calcium sulphate with added dysprosium is used in radiation dosimeters: Thermoluminescence Dosimeter, Its Manufacture And Use (1982).

Dysprosium iodide is used in halide discharge lamps in order to ensure very intense white light: Ceramic Metal Halide Lamp (2014).

References:

All patent information has been obtained from Espacenet (European Patent Office).