They do not have to pay National Insurance contributions. They stop in the week you reach state pension age – currently around 63 for women and at 65 for men. If you earn £300 a week that saves you £17.40, halving your weekly tax bill.
If you are self-employed Class 2 contributions of £2.80 a week also stop when you reach state pension age. But Class 4 – which are a tax on your profits above £8060 a year – carry on to the end of the tax year in which you reach that age. They stop the next tax year.
It is worth checking that you have indeed stopped paying when you reach those magic ages. It is after all one good thing about getting old!