How do I move to a new tab in gedit using the keyboard?

To move to the previous tab (left): Ctrl + Alt + PageUp
To move to the next tab (right): Ctrl + Alt + PageDown

Full list of shortcuts here: https://help.gnome.org/users/gedit/stable/gedit-shortcut-keys.html

Alt + Number. In fact it works with many application that have tabs

You can install Control Your Tabs plugin, then four shortcuts get added:

• Ctrl+Tab / Ctrl+Shift+Tab switch tabs in most recently used order.
• Ctrl+Page Up / Ctrl+Page Down switch tabs in tabbar order.

^{Credit to Trevor Clarke for posting this on another question}