can you purchase more space I need to update my Mac

Yes you can by installing an external disk. Then you can transfer files, such as photos or music files to the external disk and that will allow you to delete them from your HD to clear up the needed storage space. These days these disks are cost effective, compact, easy to install with vendor provided USB cables and most do not require external power. You may have to reformat it though. There is a large selection of disks to choose from. This solution will allow you to easily have the storage you need. Easy and done.

Everybody needs a couple of external drives to backup to, for just such reasons as yours, :)