I have Avast Security installed on my existing Windows 7 PC. I have bought a replacement Dell with Windows 8.1 and McAfee anti-virus installed by default. What/ how do I need to do to replace the McAfee with my Avast subscription program?
Welcome to the forum. 
May I suggest that you follow the instructions outlined in my signature to Successfully install Avast.
You didn’t mention which version you currently use. If it’s a premium (paid) version, remove it from the old computer and transfer your license information to the new
computer so it can be used there.