British and Irish Nationals in the Common Travel Area
British Citizens living in the Isle of Man
You will not need to take any action, and there will be no change after Brexit.
Irish Citizens living in the Isle of Man
Irish citizens will not be required to apply for settled status in the UK or in the Isle of Man. The Common Travel Area ensures that the rights of British and Irish Citizens are protected after the United Kingdom leaves the European Union. This preservation of the existing ability for UK and Irish citizens to move freely within the Common Travel Area also extends to those UK and Irish nationals on the Isle of Man.
Further information about UK and Irish citizens in the Common Travel Area can be found CTA Technical Notice document.