Place the almonds in a small dry skillet over medium heat and toast, stirring, for 3–5 minutes until golden; remove from heat and let cool.
While the almonds toast, remove the skin from the rotisserie chicken and discard the skin and bones; pull the cooked meat off the bones and roughly chop until you have about 5 cups.
Chop the celery, dice the apple (firm variety), and chop the scallions and fresh dill.
In a large mixing bowl, combine the chopped chicken, 1 1/4 cups mayonnaise, celery, diced apple, 1/2 cup sweet pickle relish, toasted almonds, scallions, Dijon mustard, and chopped dill.
Stir thoroughly to evenly combine; taste and season with salt and black pepper as needed. Add more mayonnaise if you prefer a creamier texture.
Cover the bowl and chill until ready to serve; chilling improves the flavor.