Drain the pickled beets thoroughly in a colander. Pat them dry with paper towels to remove any excess moisture.
Dice the beets and apple into roughly equal ½-inch (1.5 cm) pieces. Finely dice the pickles and red onion. Add everything to a large mixing bowl.
In a small bowl, whisk together the mayonnaise, sour cream, Dijon mustard, and pickle brine until smooth and combined.
Pour the dressing over the beet mixture. Stir gently to combine, being careful not to over-mix and crush the beets.
Season with salt and white pepper. Taste and adjust seasoning as needed.
Cover and refrigerate for at least 30 minutes before serving.
Transfer to a serving bowl, garnish generously with fresh dill, and serve chilled.