General preparation for all options
As with all major disk operations, ensure you have backups of important data, before beginning. Pay special attention to backing up any keys, SSL, GPG, etc on the drive as they are not included in many backup routines. I use seahorse Passwords and Keys, any keymanager should have a backup function.
Option # 1: Get Kubuntu Desktop for your flavour
sudo apt-get install kubuntu-desktop
Will add kubuntu-desktop GUI and apps, to your existing installation, you can switch between at the login. Pros, both are available. Cons, a lot of redundancy.
Option # 2: Clean install
Pros, well it's clean. Cons, time and effort reinstalling packages, and possibly data.
New information: Xubuntu, 17.04 release will provision a swap file instead of a partition swap on clean installs, upgrades in place will continue using the legacy swap partition. Check you iso release notes for your chosen Ubuntu version
Option # 3: Upgrade in place * my recommendation
Download a iso image of the desired version of Kubuntu, and put on a USB.
Boot from USB, select the first Option, Update to... Pros, clean Kubuntu GUI, the installer cherry-picks conflicting system files and removes them.
Cons: none I'm aware of
Option # 4: Install alongside your existing installation.
Not really an option for your end point.