Thats what the Mask Component is for, just add a UI Image with the Mask Component, then Parent anything you want masked to it. By default Masks Hide any part of Images that are over a transparent part of the Mask Image, so easiest way is probably to use a mask texture like this to get what you want:
(Will need to open in new window to see it since White on White background =P)
The Mask Texture has to be imported as “Sprite (2D and UI)”
After that You should be able to Untick “Show Mask Graphic” on the Mask component to only show the Ui that it covers.