Gov.uk says:
When you stop paying
If you’re employed, you
stop paying Class 1 National Insurance when you reach the
State Pension age.
The thresholds for when you start to pay tax and NIC have always been different, NIC being the lower figure. Currently, you pay PAYE tax on ANY income/earnings of £12500pa. This include any pensions you may have. The totals are lumped together, and anything over the £12500 are subject to PAYE tax. State pensions are paid gross, so the tax is taken off your other earnings. The tax code reflects this by taking off the value of the state pension from your £12500 allowance, the balance being your code number (with the last digit removed). Tax is then applied to your main source source of income.
As mentioned above, NIC does not apply to people over the state pension age - unless those rules were changed yesterday (I haven't checked). Currently, if you earn at or more than £184 per week, you start paying NIC (unless you're a state pensioner). If you earn £183.99 per week, you don't pay it.
Hope this helps. (I was a former PAYE/NIC Auditor / Compliance Officer in the Revenue for over 20 years)