Heat oven to 400° F. Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the pork with the fennel, paprika, ½ teaspoon salt, and ¼ teaspoon pepper and cook, turning occasionally, until browned, 6 to 8 minutes.
Place the pork on a rimmed baking sheet; reserve the skillet. Transfer the pork to oven and cook until an instant-read thermometer inserted in the center of each tenderloin reaches 145° F, 12 to 15 minutes. Let rest for 5 minutes before slicing.
Meanwhile, add the remaining tablespoon of oil to the drippings in the skillet and heat over medium-high heat. Add the onion and cook, tossing, until beginning to soften, 3 to 5 minutes.
Add the green beans, ½ cup water, and ¼ teaspoon each salt and pepper and cook, partially covered, until the green beans are tender, 4 to 6 minutes. Add the olives and vinegar and toss to combine.