Poach the shrimp: Bring a pot of salt water to a boil. Turn off the heat and add the shrimp. Cook for 1-3 minutes for fresh shrimp (or up to 5 minutes for frozen shrimp), until the shrimp turns pink and opaque.
While the shrimp are cooking, prepare a large bowl of cold water with ice. When the shrimp is done, immediately drain it in a colander and then transfer the shrimp to the bowl of ice water to stop the cooking process. Set aside for about 5 minutes, until the shrimp is cold.
Meanwhile, make the shrimp salad dressing. In a small bowl, whisk together the mayo, lemon juice, Dijon mustard, dill, chives, old bay seasoning, and black pepper.
Drain the shrimp and pat dry. Transfer to a large bowl. Add the sliced celery and diced red onions.
Pour the dressing over the salad. Toss to coat. Adjust salt and pepper to taste.
Serve immediately, or if you have time, refrigerate for 1 hour (up to 3 days) to let the flavors develop. Stir right before serving.