What do I do if there isn't any storage space on my Mac Air for the new update ?

See used and available storage space on your Mac

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

Guess the internal drive is the smallest size 128 GB. If so - this issue is going to be an ongoing issue all the time.

Free up storage space on your Mac - Apple Support

This issue comes up daily on this forum. It is not possible to free up the storage allocated to "Other". This is part of the operating system and is read only. Messing with it would likely make your computer inoperable. If you have insufficient space to upgrade your OS, the solution is to purchase and install an external disk which you can copy files to, which can then be deleted from your hard drive to clear space there. These disks are readily available, reasonably priced, compact and easy to install with provided USB cables. Most do not require external power. You may have to reformat it, though. This is an easy solution to solve your problem.