I am trying to move an iMac slideshow project from my photos in my iMac to my iPhone .
I want to view this slideshow on my Apple TV.
I cannot find a way to sort of export this photo slideshow from iMac to iPhone.
Device: Mac Running Catalina
If you mean the type of slideshow you get when you choose File, Create, Slideshow, then you have to export that to a video in order to share it. These kinds of "projects" are Mac-only, so you won't see them on your iPhone.
While in the Slideshow project, go to File, Export, Export Slideshow. Then save it out as a video.
Now you can share that file with your iPhone any number of ways. Yo can use iCloud Drive to access the file on your iPhone. Or, you can use AIrDrop to share it as a video. You can add it to the TV app and then see it on your iPhone or Apple TV's TV app as long as you have that enabled in iCloud on both devices.
Thank you for the easy to follow information regarding my slideshow.