By running PS4 in "Safe mode" and performing a "Data rebuild", the system will give you an option to update.
After the update, you should be able to install the live title.
Turn off the PS4 system by pressing the power button on the front panel.
The power indicator will blink for a few moments before turning off.
Once the PS4 system is off, press and hold the power button again. Release it after you hear the second beep: one beep will sound when you first press, and another seven seconds later.
Connect the DUALSHOCK 4 with the USB cable and press the PS button on the controller.
Once the safe mode is on, in the menu, follow the instructions to Rebuild your database: Go to option "Rebuild Database" and press X "The database will be rebuilt, it might take a few hours to rebuild the database" will be displayed, Select OK.
The screen will go blank whilst the Database is being rebuilt and this could take a few hours depending on the amount of saved content.
When the Rebuild has finished the console will return to the sign in screen.