Bring a large pot of water to a boil. Season with salt and add pasta. Cook according to the package directions, then drain and set aside in a large bowl.
Meanwhile in a small bowl or jar, make the dressing by whisking the tahini, lemon juice, and garlic until well combined. Gradually add water to the mixture until well blended. Stir in the greek yogurt, sumac, salt, and pepper, and continue to whisk until the ingredients are evenly distributed.
Add the dressing to the cooked pasta, then top with the chickpeas, cucumbers, bell pepper, tomatoes, olives, and parsley. Toss until everything is combined and evenly coated in the dressing.
Chill for 1 hour before serving to allow the flavors to develop.