You got it right, Nitrogen, Phosphorus and Potassium.
Nitrogen is in obviously present.
Phosphorus can come from different things you feed the fish.. I want to use black soldier flies.. dried they're 1.5% phosphorus and should end up in the plants after the fish are done with it.
Potassium also comes from fish food. Some people put pieces of banana's in their grow beds. I'm somewhat sceptical of this method, but apparently it works and probably what I'll try if I notice potassium deficiences.
Another thing that can be done with live food is feed it what you want to get into your fish and plants. My girlfriend and I eat a lot of fruit and vegetables, the left overs go in the worm bins, fish eat the worms, worms poo in the water, cycle is complete. Some people have fruit eating fish and they just feed the fish fruit with the nutrients they want in the system. Some people use a product called Seasol which is a liquid seaweed/fish fertilizer.
Iron is the biggest nutrient problem in an aquaponics system. Most people supplement with Iron Chelate, it's what I do.
The only thing I've ever added to my system is food and iron chelate.