The expiry date shown on the visa is the date by which you should leave the UK. If your visa category enables you to extend your stay, you can apply for an extension of leave.
You must be in the UK to apply for the extension and you must apply within 28 days before the end of your permission to stay in the UK.
You should obtain legal advice from a specialist immigration solicitor to find out by what method you can extend your legal stay in the UK and to find out which visa application should be submitted; it is vital to submit the correct visa application.
A fee is to be paid when you make your application and it will not be refunded if your application is refuse or if you withdraw it.