Try the game's support forums.
It's almost impossible for us to answer this without knowing anything about the game's structure or how you installed it, because your 'old version' might be a full installation or it might be a patch which is necessary to play the updated version of the game (it really depends where your save file is stored as well whether you'd lose progress, so look into backing it up before trying anything). I looked up the game and it's an Origin exclusive on PC so that is how I am assuming you are playing it. Origin supports
saving in the cloud, which means you would be able to access your save again if you messed up a file on your computer, but I can't guarantee this because I don't know if this feature is supported for your specific game. I would not, however, recommend deleting random game files before finding out which you should be deleting from a good source.
Instead I recommend you look up tips for clearing up hard drive space if you don't want to try what Minwu suggested. There are plenty of lightweight and free utilities for checking out where hard drive usage is concentrated on your computer, allowing you to identify where you can start freeing up space fastest (don't start deleting from your operating system folder, but if you see things like a giant videos folder, clear out the videos). WinDirStat is a popular one. Uninstall old games you don't play, delete old movies you don't watch, clear temporary files, get an external hard drive and move things to that, etc. etc. Having a full drive is going to bug you whether you update your game or not so you should look into that anyway.
tl;dr Minwu is right and his suggestion is good but check your game save is on the cloud or find out where the file is and back it up first
(P.S. If anyone on this forum for some reason is an expert on this game, feel free to PM OP.)