A website's address should never change, and if it does, your hosting provider should automatically update it's DNS servers to the new ip address so your domain name will always resolve correctly and you don't have to do anything. So, once your new website is fully running under its domain name, there is no reason to update the app.
But if there is a chance that the domain name needs to change for some reason, you could put an error message in your app for when it can't access the website (the old domain name doesn't work anymore) it will say "Can not access cloud service. Please check the Play Store to see if there is an update to this app.".
So, if the domain name ever needs to change, then you can simply upload a new update for your app with the new domain name and the error message in the old version of the app will direct the users to install the new update.
In summary, you should not release the app until the IP address of your website propagates so the app can access your website using the domain name.