This is a common issue that can be fixed quite easily by following the steps below;
- Turn off your PS4 by holding the power button until the system shuts off completely.
- Unplug all of the cords that are connected to your PS4 from the system directly.
- Place the PS4 vertically. The disc usually gets stuck when the console is horizontally resting. Placing it vertically may help dislodge it.
- Wait about 30 minutes.
- Reconnect all of the cords.
- Boot into safe mode by holding the power button for 7 to 8 seconds.
- Cross your fingers. That's really it. The disc should hopefully eject now.
If this has not worked, there is also a way that may resolve this, but it does require a little bit of assembly;
Tear-down Repair (I can upload a guide if needed)
- Slide down the top cover.
- Peer down the side of the hard drives, and you should locate a Flathead screw/bolt.
- Tighten this screw until it has a bit more give than it previously did.
- Cross your fingers. This is a manual eject button, just in the form of a screw.
A software reinstall would also be a good step to take if this would be a preferred route that you would rather take.