In large skillet over medium heat, brown ground beef, celery, onion, carrot, garlic, salt, and pepper, breaking up beef until browned and no longer pink, for approximately 6-8 minutes.
Add tomato paste, brown sugar, vinegar, mustard, and water; mix well. Bring to boil, reduce to simmer and cook 15-20 minutes until sauce thickens and flavors meld.
Remove from heat; taste and adjust seasonings, if necessary. Divide evenly among pita bread pockets and serve.