I run a business where I employ drivers who regularly cross the border into the EU. Can I arrange their insurance for them or will they need their own documents?  

As an employer, you will be able to arrange insurance cover on behalf of your employees, as you do today.  

However, each of your employees will have an individual legal responsibility to carry these documents. Driving for employment or business purposes would not exempt anyone from needing to carry a Green Card.

A Green Card is required to cover the registration number of the individual vehicle, so a Green Card will be needed to cover each vehicle insured under one policy when being driven in the EU.

If your employees change vehicles, they will need to carry the Green Card that is registered to the registration of the vehicle they are driving.

If the vehicle is towing a trailer, you will also need a separate green card for that trailer.