my iCloud is not updating on my MacBook Air

Try going to System Preferences/iCloud (Apple ID for Catalina or later) and stop Contacts syncing by unchecking the box. Wait a couple of minutes, then check syncing. Allow time for the sync to complete.

Last resort  - have you tried signing out of iCloud, restarting, and then signing back in?

See the Apple Support article below. 

Contacts, Calendars, or Reminders - Get help using iCloud.     

See the articles Set up and use iCloud Contacts - Apple Support

If your iCloud Contacts, Calendars, or Reminders won’t sync - Apple Support

Etherfeat wrote:

Why do my contacts on iCloud not populate onto my MacBook Air? They update on my cell phone attached to my apple id.

It sounds as though your MacBook Air is not configured to sync with contacts.