To avoid running out of space when moving backups to a new repository, the "Move backup..." function in Veeam Backup & Replication should be used. This function allows you to relocate backup files to a new repository without duplicating data, which can save space. Unlike a simple copy action, the move function ensures that the backup chain remains intact and does not require additional space for a copy of the backups during the transfer. When the move is initiated, Veeam will also automatically update the configuration to point to the new backup location, thus preventing any disruptions in the backup chain.