Upgrading / migrating from docker 1.10.3 to docker community latest version (19.03)

I am afraid you won’t find any. Your current version is a “pre community edition” version. The release notes start with 17.03, which is the direct successor of 1.13.1.

To be on the safe side, you can read the release notes for each and every CE release.

Though, if you used a volume/graph driver for your volumes that is not supported anymore, you might want to stop your containers, backup the volumes and restore them after the upgrade. This is not necessary for binds (-v /host/path:/container/path), as they are not managed by the volume/graph driver.

If you are already on overlayfs2 or btrfs you can skip the backup part. If you are on aufs or devicemapper you should definitly backup your volumes. The availability of Storage drivers depends on your OS. Also the availability of the latest Docker version is OS specific. There is no CE for RHEL or Suse, just EE, which requires a cpu based licensing (till a couple of months ago it was a per node license).