How long will asparagus soup (no cream no potatoes included) stay fresh refrigerated ? Does it freeze well

I would say few days refrigerated but also make sure you have the right temperature running and I would freeze in a nice strong ziploc bag, no problem. A tip that I have learned is that when I want any left over to last a little longer in the fridge is to drizzle olive oil on food's surface to conserve longer, it does work.

I've kept mine (vegan) in the fridge with success up to 5 days. Mine also freezes quite well, though I haven't tested that longer than about 1 month.

With no cream incorporated I should think it would freeze very well for several months, if you leave it that long!