Eythora competed at the 2012 European Artistic Gymnastics Championships in Brussels and placed 10th in the all-around with a score of 52.731, 8th on balance beam with a 11.166, and 6th with the Dutch team with a total combined score of 157.361. Later in the year, she competed at the Dutch national championships in Rotterdam and placed 2nd in the all-around, 2nd on beam, and 1st on floor.
Eythora competed at the 2013 European Youth Summer Olympic Festival along with teammates Mara Titarsolej and Dana de Groot. They placed 9th as a team, and individually, she placed 9th in the all-around and 2nd on beam. Later that year, she became Dutch national champion on every event but floor.
Eythora's international senior debut came late in the year, in a small meet in Hamburg, where she placed 1st in the all-around and 2nd with her team. She had been out most of the year due to a back injury.
At the beginning of the year, Eythora was among the gymnasts vying for a spot on the European Championships team. She competed at two qualifier meets and won both, thus earning a spot on the team. In preparation for the championships, she competed at the Ljubljana World Cup, placing 1st on floor. At the European Championships, she placed 12th in the all-around but did not make any event finals.
She later qualified to compete at the World Championships in Glasgow. There, she helped the Dutch team qualify for the 2016 Olympics by finishing 8th in the team competition. During the qualifications, she placed 28th in the all-around and was the first alternate for the finals. She qualified for the balance beam event final, but fell in the final and placed 8th.
Eythora started off the season at the International Gymnix in Canada, winning bronze on balance beam and placing fourth on floor exercise. She competed at the IAG SportEvent in May, winning every event except balance beam, where she placed fifth. She became Dutch National Champion in late June. She was named to the Dutch Olympic team in July. Eythora was chosen to represent the Netherlands at the 2016 Summer Olympics in Rio de Janeiro, where she helped the Dutch team qualify to the team final. They finished in 7th place. She also qualified into the individual all-around final where she finished in 9th place with a score of 57.632. In November, Thorsdottir won silver in the all-around at the Arthur Gander Memorial in Spain.
In February, she competed at the Reykjavik International Games, winning all-around and balance beam gold, vault and floor exercise silver, and uneven bars bronze.
In April, Thorsdottir competed at the 2017 European Artistic Gymnastics Championships. In qualifications, she qualified for the individual all-around final, the balance beam final and the floor exercise final. In the individual all-around, she started well with vault, but a fall on the uneven bars and balance beam caused her to be lower in the rankings. She finished with a good floor exercise routine, and ended in 12th place. In the balance beam final, Thorsdottir competed a clean routine and finished second behind Cătălina Ponor. In the floor exercise final, she finished in third place behind Angelina Melnikova and Ellie Downie.