if I move my photos from my macbook air to the icloud storage can I remove them from my mac hard drive without them being moved from the icloud?

Hello there, bfo4nne.

It sounds like you're trying to manage your iCloud storage to save space on your MacBook Air's hard drive. The following Knowledge Base article provides a well rounded explanation of managing iCloud storage:

Manage your iCloud storage

Thanks for reaching out to Apple Support Communities.

Sincerely.

Simple answer is no. iCloud is a syncing system, not an external storage system. If you delete them from the device/Computer they will be deleted from iCloud. For the computer, go to Photos/Preferences/iCloud. That will reduce the space required by about 90% when fully effective.