Hi there. I've FreePBX ((Red Hat 4.4) on Proxmox 4.3. On the red hat, there are no lvm groups and I want to increase partition wich is used by the system, without lost data. How can I do that?

redhat 4.4 is more than ten years old. gparted can do the job for example, if it was available. Or probably you can try parted. I would try to boot another os (form pendrive) to do that.
But first save all important data!

does it remove all data, include system? Do this steps I should follow?

* boot from another *nix

* delete partition that I want to increase

* create partition

?

But how to do system backup that I do not lose data?

no, you do not need to delete, you can resize it without deleting - if there was enough space to do that.
You can do backups onto another disk/cd/dvd/tape whatever, I don't know how much data you have.

If you're honestly running a system that's more than ten years old, which is also running PBX software for your voice system, and you DO NOT HAVE A BACKUP...you have larger problems. You should ALWAYS make backups, and test them.

In your case, the best thing you can do is to back up your configurations and data (how you do this is up to you; could be a simple matter of copying your data to a different location), and reload your system from scratch, formatting your drives as you wish. Load a CURRENT OS, and if you're going to be using Red Hat enterprise, you then need to PAY FOR IT. Otherwise, load the latest CentOS, along with a less-than-ten-year-old copy of FreePBX, and move forward.

If you have concerns (and I sure would after ten years with no backups), I'd purchase new hard drives for your system. Pull the old ones after you make a backup, and set them aside. Do your installation to the new drives, reload from backup and test. If things don't work, power down and put the old drives back in. You should only have to have a small downtime window for this.

In addition, Proxmox has a wiki that outlines the steps required to resizing a guest disk.


https://pve.proxmox.com/wiki/Resize_disks