Whisk first 3 ingredients in small bowl to blend. Gradually whisk in oil. Season vinaigrette with salt and pepper.
Trim celery leaves and chop enough to measure 1 cup. Thinly slice stalks on deep diagonal. Place celery pieces in bowl of cold water. (Vinaigrette, celery leaves, and celery pieces can be prepared 1 day ahead. Cover separately and refrigerate.)
Drain celery; pat dry with paper towels. Combine celery, celery leaves, apples, and walnuts in large bowl. Add vinaigrette and toss to coat. Season salad to taste with salt and pepper.