Pulse the chopped ham in a food processor several times, until finely minced, being mindful not go too far to the point where you reach a paste consistency. (you can also chop very finely by hand)
Transfer to a bowl and stir in the mayonnaise, Dijon mustard, relish, red onion, celery, apple cider vinegar, black pepper, and salt. Mix until evenly combined.
Cover and refrigerate for at least 1 hour to allow the flavors to blend.
Stir before serving and adjust salt or mayonnaise if needed.