Preheat oven to 400F.
Measure the stock, carrots, and leeks into a large pot. Simmer at a medium setting for 5 to 7 minutes, until carrots begin to soften. Remove vegetables, and reserve stock separately.
Add the butter to a large pot over a medium-high setting. Stir in the flour as the butter melts, and stir as the roux browns slightly, for about 3 minutes.
Stir as you add the reserved stock, tarragon, and lemon zest. Bring the sauce to a boil as you stir constantly. Once boiling, reduce heat to medium-low and simmer for about 5 minutes until the sauce is very thick and smooth.
Season with salt and pepper, and stir in the vegetables, cooked turkey, apple cubes, and lemon juice. Blend thoroughly, and pour the pie filling into an 8” x 10” baking dish. Create a slight mound in the center.
Roll out the puff pastry to about 1/4” thickness in a rectangle the size of your baking dish plus about a 1/2” around the sides.
Brush the edge of the baking dish with water and lay the pastry over it, crimping and sealing the edges.
Brush the top with the egg mixture, and cut a steam vent into the top of the pie.
You can use any leftover pastry to decorate the top or edges of the pie.
Bake for 25 to 30 minutes. The pastry should be golden brown, with the mixture bubbling hot inside.