Combine apple, onion, garlic, tomato paste, sage, celery seed, anise seed, marjoram, allspice, salt, and pepper in a nonstick skillet over medium heat. Cook and stir until softened and fragrant, about 10 minutes. Remove from heat and let cool for 10 minutes.
Place chicken thighs in a food processor; pulse until coarsely chopped. Process until ground. Transfer to a bowl. Fold in apple mixture.
Scoop 1/4 cup of the chicken mixture with a large melon baller and form into a patty. Repeat with remaining chicken mixture.
Preheat a large nonstick skillet over medium heat. Cook 4 patties until browned and no longer pink in the center, about 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer to a plate; wipe out skillet. Repeat with remaining patties.