Good afternoon Mydolly,
Welcome to the Apple Support Communities!
It sounds like you are wanting to download Live Photos from your current iPhone as you don't want them to be added to your new iPhone.
The easiest way to work with Live Photos is to stay within the Photos app with iCloud Photos enabled on your iPhone and a Mac if you have one.
With the Mac, you could export the photos that you don't want on your new iPhone to a folder on the computer or an external drive.
When you get a new iPhone and enable iCloud Photos, the remaining photos (including the special format of Live Photos) in the System Library would populate to your new iPhone.
If you do not have a Mac computer to work with, this is what I would suggest to preserve the "video" portion of the Live Photos that are currently on the internal storage of your iPhone.
- Open the Photos app on the iPhone
- Tap the Albums tab
- Tap the Live Photos album
- Tap a Live Photo to select it.
- Tap the Share button and choose Save as Video from the list of options.
- Open the Videos album, select the video you just created, and tap the Share button again.
- Tap Save to Files.
- Create a folder on iCloud Drive called Live Photo Videos and save the files in iCloud Drive.
Take and edit Live Photos
Set up and use iCloud Photos
Take care.