I don't have enough space to download the new version of safari

You cannot individually install, delete or update Safari. It is installed as part of the Mac's operating system. To update Safari, you will need to upgrade your OS if that is possible. That will require a lot of space on your HD to download. The steps to free up space on your Mac very likely will not clear sufficient needed space. What you need to do is to either delete sufficient files and apps to clear sufficient space or install an external disk which you can copy files onto, then delete them from the HD to clear needed space. These days, external disks are reasonably priced and easy to install with vendor provided USB cables, although you may need to reformat it before using it. Note - if your HD gets too full, your computer will stop working and then you've got a real problem. The external disk is an easy-to-do solution.

To increase space in general refer to Free up storage space on your Mac - Apple Support.

Optimize storage space on your Mac - Apple Support also offers some suggestions.