Live Photos don’t import to MacBook

I don't do Live Photos much, but I'll try.

But I'm not sure exactly what you mean by "imported photos." Where did these come from and how did you try to import them? Do you get something else, instead? Did other pictures get imported? Details are important here.

Since you are syncing with iCloud, for instance, Live Photos from a connected iPhone would automatically synchronize with iCloud.com and with the Mac. So, if these Live Photos came from an iPhone, do you see them in Photos at iCloud.com?

Where are you looking on the Mac? In Photos, do you see them under Media Types>Live Photos?

Is there something else you're doing?

You wrote "I setup sync for iCloud Photos"

Are you trying to sync an iPhone or iPad with your Mac? Where are the Live Photos currently?

To transfer Photos between devices, you need to set up iCloud Photos on all your devices that you want to sync. And you need to be patient.

When you first set-up iCloud Photos, all devices will upload their own photos and videos and merge them into the iCloud Photos Library, before they will download new photos from iCloud.

What is the iCloud status showing for your Mac in Photos? Look below the "All Photos" tab in Photos on your Mac. Is it showing "uploading", or "synced just now" or something else? If there are "items on this Mac only" shown in the status your Mac cannot complete the upload because of problematic items and will not download anything, until you have removed the problematic items. See this link: Check the status of your library in Photos for macOS - Apple Support

And what are your other devices showing as the status? Your iPhone or iPad may have been pausing the upload, of the battery is low. Keep the devices that need uploading to iCloud connected to a power source, and if you see a "paused" message, request that they upload now.

I second Richards recommendation to check at wwww.icloud.com in Photos, if the missing Live Photos are already in iCloud.

I am also puzzled by your mentioning of "and imported photos". I hope, you have not tried to import photos directly from your iPhone, while you are using iCloud Photos. That can break the syncing of Live Photos. You have to pick one method to transfer items between your devices and stick with it. once you have set up iCloud Photos transfer your photos with iCloud.

The manual import of Live Photos is tricky. As you probably know - a Live Photo is a pair of at least two files, a high resolution still image (HEIC or JPEG) and a video component (MOV or mpeg). There may be an additional AAE file describing any LIve effect or filter. Tese files have to be imported together or Photos cannot pair them as a LIVE photo. If you already one component of a Live Photo pair, and now try to import it again to add the missing component, that may not succeed, because the the duplicate detection on import will prevent the pair from being imported together. If you already have imported a part of a Live Photo you have to delete it from the library, before you can successfully import the Live Photo. But don*t delete any items from your library, while iCloud Photos is enabled, because you will be deleting it from all synced devices. Wait for iCloud to sync your Live Photos.