Sometimes updates just don't go to plan! There's a few things you can do to make sure the update has been successfully added so you can get playing again.
Steam (PC)
First thing is to make sure your update has been installed and you've got space for the update and game. Your game should automatically update unless you've changed your settings to manually manage them. Click here for Steam Support's article on Managing Downloads and Updates.
If you've downloaded the update but still unable to get the game to load, it's always worth closing Steam and restarting your PC.
You can also find other troubleshooting steps for Update and Installation Issues from Steam here, including how to Clear Your Download Cache and Verify Your Game Files.
If in doubt, make sure Steam is completely closed and restart your PC and Steam before trying again!
Playstation
You'll want to make sure you've got the latest update installed then restart your console. Check Playstation Support here for steps on how to check for Game Updates.