Assuming that you're under 75, you're allowed to have income of up to £9440 per year without paying tax on it. Thereafter, you pay 20% tax on all of your income (unless, of course, your total income takes you into a higher tax bracket).
So you'll pay 20% tax on the earnings from your part-time job (with a tax code of 'BR').
National Insurance has been mentioned. You don't pay NI after reaching the State Pension age (as long as you've submitted a 'certificate of age exception'). Further (unless there's a particularly high hourly rate of pay), the amount of NI payable would be very low, or probably nil, anyway. (There's no NI on earnings of less than £149 per week from any one employer).