If you like to use a cloned volume with a volume group on it, then normally you will have a problem with the VG UUID and the VG Name. The good answer there is a nice solution for the problem and you can import and rename duplicated volume groups.
To rename and generate a new UUID for the volume group on the volume use the program vgimportclone.
sudo gimportclone -n old /dev/sdb1 WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! WARNING: Activation disabled. No device-mapper interaction will be attempted. WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! Physical volume "/tmp/snap.cozRdFdC/vgimport0" changed 1 physical volume changed / 0 physical volumes not changed WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! WARNING: Activation disabled. No device-mapper interaction will be attempted. WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! Volume group "system" successfully changed WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! WARNING: lvmetad is running but disabled. Restart lvmetad before enabling it! Volume group "system" successfully renamed to "old" Reading all physical volumes. This may take a while... Found volume group "system" using metadata type lvm2
After the successfully rename of the volume group activate it.
sudo vgchange -a y
Now you can use the renamed volume group old normally as other volume groups.