Only download new email on Apple Mail app on macOS

Make Use of the Archive Function

In Apple Mail, you can Archive mail that you no longer need immediate access to, but you don't want to delete.

See the Apple Support Document: Archive emails in Mail on Mac

I want to have a fresh start with an existing email address but I don't want to delete any of my old emails.

This is exactly what Archive will do. You will have a nice, fresh start with your In-Box, but you wouldn't have deleted any of the existing email messages. If you ever need to search for them again, they are readily available.

In my personal workflow, I archive everything older than 365 days (you can set up a rule, but that's a different question). The other day, I needed a Serial Number for a scanner I purchased 2 years earlier and was able to find it within a couple of seconds. This feature works, and works well!