Lightly stir together the tuna, onion, celery, shredded Cheddar cheese, dill, and mayonnaise until well combined.
Flatten the biscuit dough to about 1/4-inch thick, and place the 8 flattened biscuits on an ungreased baking sheet. Place about 3 tablespoons of the tuna mixture on top of each biscuit, and top each with another flattened biscuit. Pinch the edges to seal in the filling.
Bake in the preheated oven until the filling is hot and the pockets are lightly browned, about 15 minutes. Refrigerate leftovers.