If you're employed, or self-employed, you're legally obliged to continue paying National Insurance contributions (at the relevant rate) up until you reach state pension age. If you've got more than one job you have to pay NI contributions for each job (assuming, of course, than you earn enough from any particular job to need to pay NI). Thereafter you can apply for a certificate of exemption from HMRC. (If you don't get that certificate your employer will still be obliged to deduct NI contributions from your pay, even though he knows that you've reached state pension age).
So you still have to continue paying contributions after you've fulfilled the '30 year' quota. Strangely however, there appears to be no specific penalty for failing to do so. If you're self-employed, and fail to pay any NI contributions, you'll receive a letter telling you how much you need to pay in order to 'catch up'. However that letter specifically states that it is not a demand for payment and that you're not actually obliged to pay that amount. (I write from experience - several times over!).
Chris