In a Proxmox environment, you may need to extend root partition if it runs out of space.
To do this, you must first allocate additional storage on the hypervisor and then configure the system to perform the necessary operations.
During a Proxmox upgrade procedure, you may encounter failures caused by insufficient disk space on the root partition, preventing the upgrade from completing successfully
Select the Proxmox node to upgrade then go to Updates section. Click Upgrade to install all available updates.

The upgrade operation fails with an error due to insufficient disk space:
You don’t have enough free space in /var/cache/apt/archives/

To resolve this issue, you must extend root partition by allocating additional disk space.
How to Extend Proxmox Root Partition Using LVM
Step 1: Check If Your System Uses LVM
Run the command df to verify if you are using a LVM volume. If the root partition shows /dev/mapper/pve-root you are using LVM.
# df -H

Step 2: Identify the Disk to Resize
Next step is to identify the physical disk to use. In the example the identified disk is the /dev/sda.
# lsblk

Step 3: Resize the Partition with parted
To expand the physical disk the recommended tool to use is parted or fdisk. Run the following command to enter parted:
# parted /dev/sda

Print the current partition table to identify the number of the LVM partition (3 in the example).

Assign all available space on the disk to the selected partition.
# resizepart 3 100%

Check the current partition table once again. The size of the partition is now changed with the additional space.

Exit from parted.
# quit

Step 4: Refresh Partition Table in Kernel
To make the kernel aware of the changes occurred to the partition table, run the command:
# partprobe
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Step 5: Resize LVM Physical Volume
After resizing the underlying partition, you need to tell LVM about the new size of its physical volume.
# pvresize /dev/sda3

To know how much free space is available in the pve volume group (VG Size).
# vgdisplay pve

Step 6: Extend the Logical Volume
Extends the pve-root logical volume to consume all available free extents in the pve volume group.
# lvextend -l +100%FREE /dev/mapper/pve-root

Step 7: Resize the Filesystem
Resize the file system to use the newly available space.
# resize2fs /dev/mapper/pve-root

Step 8: Verify Root Partition Size
Verify that root partition has been successfully extended.
# df -H

Final Step: Upgrade Proxmox Without Errors
The Proxmox node can now be upgraded without any issue related to disk space.

When modifying the root partition, ensure all commands are executed carefully to prevent service interruptions or, in extreme cases, complete system failure.