Hello, I am Keith, one of the experts on Just Answer, and happy to help you with your question.
Almost certainly your tax code for your private pension is incorrect. As you probably know your State Pension (SP) is taxable, but paid gross. HMRC usually recover the unpaid tax from your private pension by reducing the tax code from the standard 1060L to some lower number to collect the amount due on the SP. If this has not happened then your net receipts from your private pension will be being over paid.
You should always check tax codes on each and every time a new one is issued. Even HMRC admit that a large number of these codes they issue are incorrect. If yours is wrong you should take it up with the tax office which has issued it and ask for it to be corrected. My own initial coding has been wrong these last 20 years and you could have knocked me down with a feather when HMRC got it right, well nearly, this year!
If you could please advise me of the gross total State and private pension you receive I can have a stab at computing your liability. Of course, if you are in receipt of other income not taxed at source this will affect the issue.
I do hope that my response is of assistance.