Gavindale: Is this as simple as click and drag?
It might be, so there is no harm in trying, as you can always move it back.
That said, any uninstall routine will no longer work at the new location, and any Registry entries as already suggested will be broken. If savvy enough you might be able to edit such, but it can get real tricky.
So generally you are better off uninstalling and reinstalling to the new location.
To assist with that, you might be able to get away with backing up first and then overwriting, if you don't want to lose something from the original install folder.
To do that last suggestion, you would do something like the following.
1. Create a temporary folder on your 'D' drive. Maybe call it Tempry.
2. Copy you existing game folder on 'C' drive to that Tempry folder.
3. Uninstall the game on 'C' drive.
4. Reinstall the game on 'D' drive.
5. Move the game folder from Tempry to your new install location, overwriting your newly installed game there.
Of course, that will all take a good amount of time, depending on the number of files & sizes for the game. But it may be worth doing.
The only other question, is whether you had installed the game via Offline Installers or via Galaxy?
If so, then Galaxy settings could be compromised.
That said, Galaxy might have a migrate option, meaning you could avoid doing the steps I mentioned.
In fact Galaxy might be able to help you anyway, even with Offline Installer installations of a game.
I don't have a lot of experience with Galaxy, don't like it, but plenty of others should be able to help you.