Bring a large pot of salted water to a boil and cook chickpea pasta according to package directions, adding the asparagus pieces during the last 2 minutes of cooking.
Drain the pasta and asparagus, then rinse under cold water to stop the cooking process and cool immediately.
In a small mixing bowl, whisk together the Greek yogurt, lemon juice, olive oil, Dijon mustard, dill, salt, and pepper until a smooth dressing forms.
In a large serving bowl, combine the cooled pasta and asparagus with the cubed chicken, edamame, peas, and sliced radishes.
Pour the dressing over the salad components and toss thoroughly with large spoons to ensure even distribution.
Serve immediately or refrigerate for up to 2 hours to allow flavors to meld.