How do you update if your space does not allow

Use Disk Utility to erase an Intel-based Mac

How to reinstall macOS

Follow these guidelines during installation:

• If the installer asks to unlock your disk, enter the password you use to log in to your Mac.
• If the installer doesn't see your disk, or it says that it can't install on your computer or volume, you might need to erase your disk first.
• If the installer offers you the choice between installing on Macintosh HD or Macintosh HD - Data, choose Macintosh HD.

How exactly are you trying to delete or erase?

You can't erase the drive from which you are operating.

Deletions, moving files to Trash and emptying, should be no problem. Are you getting any error messages?

Here is a guide to help us help you: Writing an effective Apple Support Commun… - Apple Community

Please provide added details as the guide specifies.