When you change the address on your driving license, you must remember to also change the address on your digital tachocard. Also, it is a legal requirement that you keep your old digital tachocard for a duration of up to 28 days after you have recieved the new one. 

The application procedures may vary depending on the type of license that you hold. For further information on the procedures visit:

http://www.direct.gov.uk/en/Motoring/DriverLicensing