The draft EU withdrawal agreement published on 17 November will (in the –possibly unlikely – event of UK Parliament ratification) preserve the status quo during the Transitional Period (which runs to 2020), during which time there will be negotiation of a longer term arrangement.
If the agreement fails, then upon a ‘no deal’ Brexit, we would be looking into the abyss of remaining EU based businesses having to put in place formal contracts with their UK subsidiaries or suppliers in order to transfer personal data.