Following article 45 or GDPR, The European Commission is conducting a data adequacy assessment of the UK. If the EU grants positive adequacy decisions by 1 January 2021, it would mean that personal data can flow freely from the EU/EEA to the UK, as it does now, without any action by organisations.
Article 71(1) of the Withdrawal Agreement contains provisions that continue to apply EU data protection law to certain ‘legacy’ personal data in the event that the UK has not been granted full adequacy decisions by the end of the transition period.
Otherwise, GDPR provisions for third countries may apply. You are strongly encouraged to closely monitor these developments and follow the advice provided here: https://www.gov.uk/guidance/using-personal-data-in-your-business-or-other-organisation-after-the-transition-period