Unless you have some number of websites defined via ISPConfig that are bound to specific IP addresses (instead of "*"), I'm not sure anything will fall apart. Your virtual hosts should continue to function regardless of which IP addresses are associated with them.
If, on the other hand, you have specific IP addresses assigned to any of your websites, you will need to add the new/replacement IP addresses in System -> Server IP Addresses, and once the new IP addresses are pointed to your server, you will need to change the IP Address drop-down menu for each site accordingly.
How can I check and add/change the servers' linking?
I remember adding some permissions inside the database.
I'm not sure what you mean by this. Perhaps you set some MySQL permissions for certain IP addresses in MySQL's `user` table, in which case you should log-in as the root MySQL user and have a look. Leave those records as they are, and insert new, equivalent records with the new IP addresses. Once all IP addresses are resolving correctly, you can delete the obsoleted records.
EDIT: Sorry, I missed the "multiserver installation" part. I'm not sure how much of my post will be helpful to you, but I'll leave it up.