If you decide to move out of the UK when you’ve started enjoying pension payments, you need to alert the pension service of your decision.
Normally, State Pensions are paid worldwide irrespective of the country you chose to live. However, for you to enjoy the yearly increases you need to retire in a country that has a social security arrangement with the United Kingdom or a country within the European Economic Area (EEA) including Switzerland or Gibraltar. The other option is for you to live in the UK for 6 months each year.