It depends on which older version was used. Some things have changed over the years.
If you have A) a complete backup of the site including the gpEasy system and B) a test environment,
you can simply try the following:
If you have all the gpEasy files + directories (/addons, /data, /include, /themes) you don't need to install gpEasy.
Just copy it to the server and make the /data folder (and all it's subfolders and files) writable and it should run.
Upgrade from 2.3.3 to 4.4: I'm pretty certain this will not work by just replacing the /include folder.
Data structures have changed since and I'm afraid they are not fully compatible.
But if you want to try make sure to keep your backup of the working copy of 2.3.3!