Hi Larry,
I'm unaware of any known issue that would result in clipped layers not drawing in the layout (as expected), but drawing in the printed map or the exported file.
There may be something specific about your map, layout rendering, export options, etc... that results in the clip being ignored. Can you contact Esri Support? They are better equipped to handle troubleshooting steps and gather bug data. They can be contacted at https://support.esri.com/en/contact-tech-support.
Thanks,
Tom