The Government has discussed arrangements with the EU for UK nationals travelling to the Schengen Area. Regrettably, the EU has consistently maintained that UK nationals will be treated as Third Country Nationals under the Schengen Borders Code from 1 January 2021. UK nationals will only be able to travel visa-free for short stays for up to 90 days in a rolling 180-day period. This is the standard length of stay that the EU offers to nationals of eligible third countries that offer visa-free travel for EU citizens, in line with existing EU legislation.
UK nationals planning to stay longer will need permission from the relevant Member State. This may require applying for a visa and/or permit. Information about travel to Europe after the transition period is available on gov.uk: https://www.gov.uk/visit-europe-1-january-2021