Golovkina began the 2013-14 season on the JGP series, placing 16th in Estonia. In November 2013, she won the junior bronze medal at the NRW Trophy before making her senior international debut at the Warsaw Cup; she placed 9th in the short program, 1st in the free skate, and 4th overall in Warsaw. Continuing on the senior level, she finished 4th at the 2014 Toruń Cup and 5th at the Hellmut Seibt Memorial.
2014–15 season
Golovkina competed at one JGP event and then won her first senior international medal, silver, at the Ice Star in Minsk, Belarus. In November 2014, she began competing on the ISU Challenger Series (CS), placing 5th at the Volvo Open Cup before taking bronze at the Warsaw Cup. She placed 7th at her final CS event, the 2014 Golden Spin of Zagreb. Golovkina was named to Lithuania's team to the 2015 European Championships in Stockholm, Sweden. Ranked 23rd in the short program, she qualified for the free skate, where she placed 17th, lifting her to 19th overall.
2015–16 season
Golovkina won her second Lithuanian Championship title and secured her second consecutive silver medal at the Ice Star competition in Minsk, Belarus. Subsequently, she represented Lithuania at the European Championships, finishing in the 16th position. Golovkina also participated in the World Championships, landing in 33rd place.
2016–17 season
She competed in four distinct events, with her most notable achievement being a 9th place finish in Nice.
2017–18 season
Golovkina sustained an injury that required leg tendon surgery, preventing her from participating in most competitions that year. However, she attempted to qualify for the Olympics at the Nebelhorn Trophy competition in Oberstdorf, Germany, towards the end of the season. She placed 19th and did not qualify for the Olympics.
2018–19 season: Initial retirement
During the 2018-19 season, Golovkina decided to conclude her ice skating career. She relocated to Newcastle Upon Tyne, United Kingdom, where she commenced her studies in Sports, Exercise, and Nutrition. That same year, she resumed skating at the Whitley Bay ice rink and began training under the guidance of her coach, David Richardson.
2019–20 season: Return to competition
Golovkina made a comeback to the sport after an absence of a year and a half. She began her season with a 3rd place finish in the Tayside Trophy and a 7th place finish in the Torun Cup. Additionally, she competed in the European Championship, finishing in 26th place. Golovkina won her third Lithuanian Championship title.
2020–21 season
The 2020-21 season was cancelled due to the COVID-19 pandemic. In the same year, Aleksandra decided to relocate to Dundee, Scotland, and train there.
2021–22 season
At the start of the 2021-22 season, Golovkina again competed at the Tayside Trophy competition in Dundee, Scotland, where she finished in 4th place. Later in the season, she competed in the European Championship in Tallinn, Estonia and advanced to the free program. She finished in overall 21st place. Golovkina also won her fourth Lithuanian Championship title.
Aleksandra Golovkina takes 1st place at the Tayside Trophy 2023
Golovkina began her season by participating in the 2023 Nepela Memorial, where she finished in 11th place. A few weeks later, she won the Tayside Trophy with a score of 151.23. Later in the same month, she placed second at the Swiss Ice Skating Open 2023.
At the Warsaw Cup 2023 in Poland, Golovkina set a new overall personal best of 158.67, as well as a new personal best in the free skate. In early December, she competed at the Edusport Trophy, scoring a total of 158.50 points and winning the bronze medal. In the same month, just before Christmas, Golovkina competed in the Lithuanian Figure Skating Championship, finishing in second place behind Meda Variakojyte. However, as Golovkina had the better overall results, she was still chosen to represent Lithuania at the 2024 European Figure Skating Championships.[2] This was the first time in her senior career that she did not win a gold medal at the national championships.
At the beginning of 2024, Golovkina took part in the European Figure Skating Championships, which were held in her home country, Lithuania, in the city of Kaunas. Despite a leg injury limiting her on-ice training time and a fall on her second jump,[3] she qualified for the free program in 14th place and set a new personal best for the short program. In the free program, she finished 16th and was also 16th overall in the competition.