How do I restore live photos?

A Live Photo is a pair of at least two files.

1. One file is a high resolution still frame - typically a JEPG or HEIC file.
2. The second file is the video component - typically QuickTime movie or MP4 movie with the codec HEVC or H.264.

Both components should have the same filename, but a different filename extension. There could be additional sidecar files the filename extension AAE or XPM.

When you reimport a Live Photo you have to import both parts of the Live Photo at the same time, only then Photos can combine them again to a Live Photo. If you previously just reimported the still frames, you have to delete them completely, even from Recently Deleted, before you try to reimport the pair of the still frame and the video clip. There must not be a single component of the pair already on your device, or the duplicate detection will prevent the reimport of both components together and the two components will not combined into a Live Photo.

Thanks to exiftool forum member greybeard, I learned that the key metadata item in Live photos is ContentIdentifier. It has to be identical in both the image and the movie. Even the file names do not have to match -- Photos.app shows only the imported image's filename. Also the matching movie can be from a completely different footage such as .mp4.

======== ./IMG_2158.JPG
[Apple]         ContentIdentifier               : F906FE4C-506A-4F85-B9BE-5F862ED06C90
======== ./IMG_2158.MOV
[Keys]          ContentIdentifier               : F906FE4C-506A-4F85-B9BE-5F862ED06C90

So if all metadata is stripped from from that pair and renamed as a.jpg and a.mov, they can be made a Live Photo pair again:

Copy Apple makernotes from some other Live Photo image -- IMG_2160.JPG in the example below (currently exiftool can write Apple makernotes in images only as a block, not as individual tags):

exiftool -overwrite_original -TagsFromFile IMG_2160.JPG '-All:All<All:All' a.jpg

Then copy Apple:ContentIdentifier from either image (IMG_2160.JPG or a.jpg) to Keys:ContentIdentifier in a.mov:

exiftool -overwrite_original -TagsFromFile a.jpg '-Keys:ContentIdentifier<Apple:ContentIdentifier' a.mov

exiftool -a -G1 -s -ContentIdentifier .                                                                 
======== ./a.mov
[Keys]          ContentIdentifier               : DBDA7F31-8133-4E79-8A2E-35624C26EABB
======== ./a.jpg
[Apple]         ContentIdentifier               : DBDA7F31-8133-4E79-8A2E-35624C26EABB

macOS 14 Sonoma Photos.app imports both the edited "a" and the donor "IMG_2160" pairs OK.

https://exiftool.org/forum/index.php?topic=15628.msg84864#msg84864

Perhaps if you gave more details about exactly what you did and what sort of "external clouddisk" you used, somebody here might be able to guess where in the process the video portion was lost and whether there is any hope of recovering it.