I want to transfer my Old MacBook Pro to my new MacBook Air but older model does not have enough storage to update to newest OS

The only fix for this will be to offload a sizable chunk of data to an external drive and then erase it from your startup drive. Anything in your home folder is fair game for transfer. Pictures, movies, documents and downloads are easy to transfer and usually take up the most space on a drive.

Other things you can do…

• Empty the Trash in the Dock. 

• Empty the trash in the Photos app.

• Delete unused and unneeded application installers from your downloads folder and desktop.

• Transfer files that you don’t use daily to an external drive and then delete them from the startup drive and empty the trash. Files that take up the most room are movies, images and music.

• If you use Time Machine to backup your Mac, you can force it to delete local snapshots:

About Time Machine local snapshots - Apple Support

• Use Disk Utility to delete APFS snapshots:

View APFS snapshots in Disk Utility on Mac - Apple Support 

This from Apple on the subject of freeing up space:

Free up storage space on Mac - Apple Support

Although the article says to update the OLDER Mac to the latest MacOS, you should take that as merely a strong suggestion, to reduce side-issues. Generally, those sorts of issues are rare. It is NOT a strict requirement for the Migration.

Readers report great results from using the BACKUP drive from the old Mac, rather than the old Mac itself.