Kostornaia's international debut was in early October 2017, at a 2017–18 ISU Junior Grand Prix (JGP) competition in Gdańsk, Poland; ranked first in the short program and second in the free skate, she won the gold medal by a margin of 1.36 points over the silver medalist, her training partner Daria Panenkova. She won silver behind Sofia Samodurova at JGP Italy by a margin of 0.04 points. Her placements qualified her for the 2017–18 Junior Grand Prix of Figure Skating Final, where she won silver, placing second in the short program and first in the free skate. At the senior level, Kostornaia won bronze at the 2018 Russian Figure Skating Championships. She later won silver at the 2018 Russian Junior Championships behind teammate Alexandra Trusova by a margin of 0.58 points.