Start by boiling the diced potatoes and carrots in a large pot of salted water until they are tender, but still firm, about 10-12 minutes. Drain them and let them cool completely.
In a large mixing bowl, combine the cooked and shredded chicken breast, diced onion, cooked peas, and the cooled potatoes and carrots.
In a separate bowl, prepare the dressing by mixing together the mayonnaise, mustard, sugar, vinegar, and salt until well combined.
Pour the dressing over the salad ingredients in the mixing bowl and gently toss everything together until evenly coated.
Once the salad is well mixed, cover the bowl and refrigerate it for at least 1 hour to allow the flavors to meld together.
Before serving, give the salad a final toss to ensure the dressing is evenly distributed.
Serve the chicken salad chilled as a delicious side dish or light meal.