I take it you mean Avast Premium Security ?
What is your operating system (version), what is monitors screen size and resolution ?
I'm using Avast Antivirus (free) and that is almost the reverse to yours, the UI screen has plenty of space (too much for the components I have installed). That said, I haven't seen many Avast Premium Security users reporting the same problem.
Unfortunately, I can see zero hooks to drag and resize the UI Screen, as is common with many other program interfaces.
Are you opening the UI from the Avast Tray Icon or an Avast desktop shortcut