UK already has many trade agreements with non EU countries and many will come into play after January the 1st when the transition period for Brexit is over.
The UK has already left the EU and we are now by the end of the transition period so EU trade agreements for 3rd country trading are still valid. This will change starting January the 1st so these agreements will not apply. UK is currently trying to reproduce the same agreements with these countries otherwise if no agreement is reached till the end of the year WTO terms will apply when trading with those countries.
Already agreements have been signed with a great number of countries such as Andean countries, Chile, Central America, Cote d’Ivoire, Faroe Islands, Georgia, Israel, Jordan and more Click here for full list and details
Trade agreements with Iceland and Norway though signed they will not take place as these countries are influenced by their EEA member state status. UK currently is trying to find the most effective way to reach a new trade agreement with these countries.
A Free trade agreement is also signed with Japan and there are currently a lot of agreements still in discussion.