Now that the UK has left the EU, there is a transition period during which post-Brexit arrangements will be negotiated. This period runs from 31 January 2020 until the end of 2020.
During the transition period, there is no change for UK drivers to drive in the EU, provided they have cover to drive abroad as part of their car insurance policy.
You won’t need to carry a Green Card in the EU until later in the year.
The Association of British Insurers has also issued some generic guidance on its website for driving and travelling during the transition period.