If your paper license is the old style then you can still hire a car as long as the license itself is still valid. If you only have the paper part of a new style license, you will not be able to hire a car as they will need the photo card as ID.
If you already hold a paper counterpart, after 8 June 2015 it will no longer have any legal status. You should destroy your paper counterpart after this date but you still need to keep your current photocard driving licence.
These changes only affect UK Driving Licence holders renting in the UK.All other renters are unaffected by this change as are UK Driving Licence holders renting overseas.
More details on the change, please click here.