How to Keep a Continuous Gradient After Splitting Shapes in Illustrator

Hi,

Is there a way to cut a shape into another shape e.g. circle but keep the gradient as on the example on the left rather than having Illustrator re-applying the gradient into each part of the resulting new shape? Can the gradient despite the new cut-out shape still be continuous as it is on the left? I’ve tried applying a clipping mask with a larger shape with the continuous gradient etc. but nothing has worked. The result turns withe.

Thanks.