with Path selection tool (A), select the circle you just made, copy-paste it (Ctrl-C, Ctrl-V), scale down a bit (hit Ctrl-T and resize with your mouse holding Shift). Then change path mode to Substract.
Switch to Pen tool (P), change mode to Substract, then carefully add a shape that hides unnecessary part of circle.
I wanted that the rainbow is cut 2-3 pixels before it connects to cloud. It is very easy to do: select layer with cloud, switch to Path selection tool (A), select the circle that touches the rainbow, copy it (Ctrl-C).
Then go back to the layer with rainbow, click a rainbow path to select it, paste (Ctrl-V), scale up a bit (Ctrl-T, then resize with the mouse holding Shift), and finally, change path mode to Substract.
Now that one color is ready, repeat these steps to create another color.
And another and another, until the rainbow is ready.
Now you know how to create rainbows - why not add some more?