You do not pay National Insurance (external link) after you reach State Pension age (external link) - unless you are self-employed and paying Class 4 contributions.
You only pay Income Tax (external link) if your taxable income - including your private pension and State Pension - is more than your tax-free allowances (external link) (the amount of income you’re allowed before you pay tax).
You must contact HM Revenue and Customs (external link) (HMRC) if you think you should be paying tax.