How Can I Add a TV to My PC Setup with No GPU Ports Left?

You have a few options here! One way is to upgrade your GPU to one that supports four monitors. If that's not an option, consider using a KVM switch to alternate between one of your existing monitors and the TV. Alternatively, you could just use two monitors with the TV instead. Another idea is to plug in a Fire Stick; if your TV is a smart one, you might be able to use it as a wireless monitor. Just keep in mind that your graphics card might not handle this easily if you're trying to drive all the displays at once.

You should look into a DisplayLink dock if you're open to that, though it might not be the best solution. I would recommend getting a GPU that has at least four ports instead. It'll be much simpler in the long run.

If your GPU has DisplayPort, you could daisy chain monitors to free up a port for your TV. Just keep in mind that it could either extend your display or mirror it, depending on how you set it up.

I was curious why you're running a CPU without internal graphics. Most motherboards have that option nowadays. Can you confirm that? Maybe your CPU just doesn't support it, but it's worth checking.