Your current SSL Certificate will expire as soon as the “Next Due Date” for your SSL Certificate passes. If you keep your old and expired SSL Certificate on your website, then all the web and mobile browsers will show your website as insecure and will prompt users that your website has a major security problem, and will not let visitors enter your website unless visitors explicitly accept to enter your website on their own risk. You can see an example of these security alerts that visitors will see on your website if you keep an expired SSL Certificate.
The solution to prevent that is to renew your SSL Certificate, and install the newly renewed SSL Certificate on your website. In that case your website will continue to show as secure.
The other, less preferable solution, is to uninstall the SSL Certificate from your website. In that case, visitors will be able to see your website. They will not be stopped from viewing your website as shown in the screenshot from above. However, so as your website will not have an SSL Certificate in general, then visitors will see the “Not secure” message in the browser’s URL bar next to the name of the website.