Place the potatoes on a sheet pan. Pour 2 tablespoons of olive oil over the potatoes. Sprinkle the potatoes with salt and pepper.
Roast the potatoes for 20 minutes.
Add the olives, garlic, and remaining 1 tablespoon of olive oil to the potatoes, gently stirring to coat the ingredients in the oil (a metal spatula works well). Return the pan to the oven for 15 minutes, until the garlic is toasty and fragrant, the potatoes are soft, and the olives are warm.
Spoon the potatoes, olives, garlic, and olive oil remaining on the sheet pan into a large bowl. Add the arugula and squeeze the lemon juice over the top. Toss to combine the ingredients. Top with the lemon zest. Serve warm. The arugula will wilt.