Peel any tough fibers from the celery stalks and slice the stalks on the diagonal into pieces about 1/8 inch thick by 1 inch long. Cut the fennel bulbs in half lengthwise, then slice them crosswise 1/8 inch thick. Transfer the celery and fennel to a bowl of cold water and refrigerate.
In a small skillet, toast the nuts over medium heat for 3 to 4 minutes, shaking the pan for even browning. Transfer the nuts to a plate to cool.
In a salad bowl, combine the lemon juice, mustard, garlic, honey and salt. Whisk in the olive oil and season with pepper.
Quarter and core the apple. Cut each quarter into 2 wedges. Thinly slice the wedges crosswise. Add the apple slices to the dressing and toss well to coat.
Drain the celery and fennel and dry in a salad spinner (or blot dry with a paper towel). Add the celery and fennel, celery leaves and walnuts to the apples and toss. Serve immediately or refrigerate for up to 1 day.