Yes, you can! The Xbox One Elite Controller allows for interchangeable thumbsticks, directional-pads, and back paddles. You can purchase additional parts from sellers like Amazon or from Microsoft’s website. For instructions on how to replace the thumbsticks, reference the Thumbstick Replacement Guide.
The Xbox will allow you to customize your controller’s paddles (along with other buttons). What you will need to do is download the Xbox Accessories App. You can download the app on your Xbox by navigating to the 'Apps' tab on the Xbox dashboard. Then, in the ‘Search all apps’ bar, type in Xbox Accessories. The screen should display the Xbox Accessories App under ‘TOOLS’ which you can then click on and install. Once it’s downloaded, make sure to pin it so it will appear on your homepage. Finally, navigate back to the dashboard’s homepage and it should appear as one of your apps. As an alternative, you can use a PC to customize the paddles by downloading the Xbox Accessories App onto your computer; however, it requires that your operating system is Windows 10.
There are several reasons your controller might not be connecting to your Xbox One. Usually, the controller won’t connect if the batteries are low or completely drained. If replacing the batteries has no effect, refer to the Xbox One Wireless Controller Troubleshooting Guide for more solutions to your problem.