Will the incremental backups just continue or do I have to do a full backup (filling up the new disk as well) first?
It depends on your rotation settings - the number of backup days at Step 6. Specify Local Storage Settings
. It the retention limit is reached the restore point is going to be merged into full backup according to the existing logic Backup Retention Policy
, but if there is no free space left for a new incremental restore point the backup job will simply fail.
Indeed you can use Backup to Rotated Drives
mechanism which will require more than one USB drive to be used as a backup destination.