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Your ESA will end when your State Retirement Pension starts to be paid.
Although you would not be able to make a new claim for PIP, you will still be 'invited' to claim PIP at some stage as you are in receipt of DLA. The process is very much behind schedule!
If your PIP claim is refused you would be able to make a new claim for AA. Please be aware that there are only 2 levels of AA daily living award and no mobility element.