Maybe.
You can move (i.e. copy and subsequently delete the original) installer app to the external hard disk drive, which will increase some space after you empty the Trash, but the total amount of free space required to actually accomplish the installation is greater than that of the installer app itself.
For reference:
Optimize storage space on your Mac - Apple Support
Free up storage space on your Mac - Apple Support
After deleting whatever files you can live without and emptying the Trash, you need to wait a while before the Finder decides sufficient space exists to accomplish the installation. "A while" has been anecdotally reported to be as much as 24 hours, although I have been unable to personally confirm those reports.
There is a workaround. Consider the following.
If you are still unable to create sufficient space for the upgrade after exhausting the above steps, the workaround is to create a Time Machine backup, completely erase the Mac, install the latest version of macOS (read • below), and finally transfer the contents from that Time Machine backup when asked. To learn how to use Time Machine please read Back up your files with Time Machine on Mac - Apple Support.