Renew Push certificate and keep current App Store App working

The push certificate cannot be renewed. You have to create a new one.

The push notification certificate is not part of the application build. Therefore for push to continue working you only have to create a new certificate and deploy the p12 file (or whatever other format you are using) at your server. You don't have to submit a new version of your app.

You cannot renew an existing push certificate. You just create a new one. But you don't need to. You'd better create a push notifications auth key. You can use it the same way as the certificate, but it doesn't expire and there is no need to renew it every year.

You create the push notifications key from the Member Center, Keys tab: