Assuming you’ve downloaded a trial copy of avast premier, and ensured Windows Defender is off and disabled, you should not have any issues with installing.

You don’t say if you have a paid licence or not.

If this was an upgrade from Windows 7 or Win 8 or 8.1, this is not mentioned either, because if an antivirus is already installed and carried over it would interfere with proper installation of Premier in Windows 10. Did you try uninstalling the old antivirus program brought over from the old operating system before attempting to install Premier? Did you reboot after uninstalling?

This could be the cause of your warning window.

[EDIT:] What is AVAST Premium? Avast does not offer this program. https://forum.avast.com/index.php?topic=174286.0
[EDIT II:] Appears softonic site offers Avast Premium (don’t go there) (and also appears to be AVG antivirus, not avast) and several cracked key(gen) sites available here: https://duckduckgo.com/?q=AVAST+Premium