For the pickled fennel: Quarter the fennel bulb and cut out the core. Slice thinly across the fiber into quarter circles. In a medium bowl, toss together the fennel, salt, orange zest, orange juice and cider vinegar. Cover with plastic wrap and let sit at room temperature for about 15 minutes. At this point, the fennel is ready to use or it can be stored in the refrigerator for up to a week.
For the salad: In a large bowl, toss together the arugula, olives, apples, pickled fennel with its juices, and olive oil. Toss gently with your hands or a wooden spoon.