Is there a keyboard shortcut to open a new Konsole tab?

Works for me (in Kubuntu):

System Settings -> Shortcuts and Gestures -> Custom Shortcuts -> right-click -> New -> Global Shortcut -> Command/URL -> type a name (i.e. "Terminal" or "Konsole") -> choose tab "Trigger" -> click on None -> press Ctrl+Shift+T -> choose tab "Action" -> enter "konsole" for Command/URL -> apply

By default this combination (Ctrl + Shift + T) works in Ubuntu, but not in Kubuntu.

In Plasma, the shorcut is disabled by default in example custom shorcuts:

Have to create a custom global shortcut from the system settings for the kubuntu.

Here's how I assigned a shortcut to open the terminal (Konsole) demonstrated:

1. Right-click on the Kickoff Application Launcher icon (in the left bottom corner of Desktop scene)
2. Hit on Edit Applications...
3. Expand System
4. Hit on Konsole (Terminal)
5. In right-side click on Advanced Tab
6. In Current Shortcut Key set a new shortcut (Ctrl+Alt+T)

Try it.