How to add a volume to current in use MySQL database

related to the problem I faced here No space left on device, I want to adopt a long term solution about the point no space left on device. One of the action includes to add a volume to the machine in which the database runs (MySQL 8, Ubuntu 20.04 and Digital Ocean provider).

I would like to know which one is safest way and rules to follow in order to avoid loosing reference and/or data when I will add a volume on the machine. Considering that this database is running in production without any replication.

Thank you in advance for the support