My situation: there was RAID setup between 3 physical hard disks, however one of them was considerable bigger – about a couple of TBytes.
I needed the additional space for other purposes so I needed to create a new partition and ideally avoid rebooting the server.

The plan is to create an extended partition that will contain a logical Linux partition mounter to a new folder

Identify where to create the new partition, in my case sdc:
fskdisk -l

creating an extended partition

fskdisk /dev/sdc
type p (to print the partition table)
type n (new partition)
press enter (it will take the default value)
press enter (it will take last cyclinder as default value)
press w (saving the partition)

to avoid reboot one may try
partx -v -a /dev/sdc

creating a linux type partition from the extended one we creted

fskdisk /dev/sdc
type p (to print the partition table)
type n (new partition)
press enter (it will take the default value)
press enter (it will take last cyclinder as default value)
press w (saving the partition)

mkdir /backup_extern
mount /dev/sdc5 /backup_extern