Whisk the olive oil, white balsamic vinegar, minced olives, grated garlic, lemon zest, and red pepper flakes together in a small bowl until well combined.
Bring a large pot of salted water to a boil and add the quartered potatoes, simmering them for about 5 minutes until just tender.
Remove the potatoes with a slotted spoon and place them in a large mixing bowl, keeping the water in the pot for the green beans.
Pour 2 tablespoons of the vinaigrette over the warm potatoes and toss gently to coat.
Return the pot of water to a boil, add the green beans, and cook for 2 minutes before draining and immediately plunging them into a bowl of ice water to stop the cooking.
Drain the cooled beans well and add them to the bowl with the potatoes along with the cherry tomatoes, sliced fennel, and red onion.
Pour the remaining vinaigrette over the vegetables and toss everything together to combine.
Fold in the arugula just before serving and top each portion with a piece of the prepared salmon.