Drag the gradient fill from the Fill box in the Tools panel or Color panel to the Swatches panel. In the Gradient panel, click the gradient menu (next to the gradient box) and click the Save To Swatches Library icon .

How do you save a gradient?

Select the shape → Click on Swatch Libraries Menu in Swatches Panel → Click on User Defined → Select Your Saved Gradient. This is how you can save a gradient permanently and use it in other artworks.

How do you save a gradient to a CC library?

At the moment Gradients and Patterns are not supported by the Cloud Libraries. But as a workaround, create obects and fill them with gradients and patterns. Drag (add) those objects to a CC library. When you want to use them in another document, Alt drag them from your library to place them embedded.