FWIW If it were me, I would stop elasticsearch & kibana (& logstash if this is the only elasticsearch node in the cluster) then move the old data dir to a new location out of the way:
sudo mv /var/lib/elasticsearch /var/lib/elasticsearch-old
Then set up the new volume (which should be at least 15% larger than the size of the indexes you have on disk as elasticsearch won't create new indexes on a disk with less than 15% free space) with a file system and find out it's UUID and get ready to mount it:
sudo fdisk /dev/sdX # New volume, use all the space
sudo mkfs.ext4 /dev/sdX1
ls -la /dev/disk/by-uuid/ | grep /dev/sdX1 # Or forget the grep and manually look for it
Then add the following to your /etc/fstab, replacing with the UUID from previous command:
UUID=<RESPONSE> /var/lib/elasticsearch ext4 defaults 0 0
Make the new directory as the old one is gone, it probably wants chowning (I assume the owner should be elasticsearch but you can confirm by checking ownership of the old folder) and you want to copy the content from the old one:
sudo mkdir /var/lib/elasticsearch
sudo chown -R elasticsearch: /var/lib/elasticsearch
cp -rp /var/lib/elasticsearch-old/* /var/lib/elasticsearch
Once everything has finished copying across you should then be able to start elasticsearch back up, it should find the indexes as they haven't moved, config doesn't need updating.
Once you're happy that everything is working you can delete /var/lib/elasticsearch-old and reclaim your space. Failing that you can revert to the old data and it should continue to work.