Yes, that will be no problem.
You will need to remove avast from the previous system and install it on the new one.
On the new one just enter your current license and it will work.

You may have to remove your current system from your account first.
https://my.avast.com

If you want to keep using avast on your current system as well as on your new one, you will need two licenses.
Either paid or free.