Finely chop the dill pickles to approximately 3mm pieces. Roughly chop the drained capers.
Combine the mayonnaise, pickles, capers, lemon juice, Dijon mustard, fresh dill, and chives in a medium bowl. Stir with a spoon until evenly combined.
Season with salt and white pepper. Taste and adjust: add more lemon juice for brightness, a pinch of salt if flat, or a splash of pickle brine for extra acidity and brine without thinning the sauce.
Cover and refrigerate for at least 30 minutes before serving. Store in a sealed jar in the fridge for up to 5 days.