When the text is too long and overflows the frame, Scribus displays a small red square at the bottom right.
If you want the text to continue in another frame, you can create a link between frames:
You can also create a link to an existing frame (on the same page or on the next page) but it is imperative that the second one does not contain any text:
To remove the link between frames, use the "unlink" tool placed just after the link tool and follow the same procedure, but first click on the second frame, then on the first one.
A little hint: to link the frames, you can also click on the overflow mark, without first activating the link tool.