At the 2013 Valentine Junior World Cup, Ashirbayeva won silver in clubs, bronze medals in hoop, ball and ribbon.

In 2014 Season, Ashirbayeva began competing in senior tournaments appearing at the 2014 Holon Grand Prix, she finished 4th in the all-around.

In 2015, Ashirbayeva started her season at the 2015 Moscow Grand Prix, competing in the international tournament division finishing 5th in all-around behind Israel's Linoy Ashram.

Ashirbayeva won 2 bronze medals (hoop, clubs) at the 2015 Asian Championships in Jecheon, South Korea.

[9] On March 17–20, Ashirbayeva then competed at the 2016 Lisboa World Cup where she finished 10th in the all-around with a total of 69.700 and qualified to ball, ribbon finals.

[11] On July 1–3, Ashirbayeva competed at the 2016 Berlin World Cup finishing 8th in the all-around with a total of 70.250 points, she qualified for the hoop, ball and clubs final.

On March 31 – April 2, Ashirbayeva competed at the 2017 Grand Prix Marbella finishing 19th in the all-around and qualified to 1 apparatus final.

On April 7–9, Ashirbayeva competed at the 2017 Pesaro World Cup finishing 9th in the all-around and qualified to 1 apparatus final in clubs.

Ashirbayeva's next event was at the 2017 World Challenge Cup Guadalajara where she finished 4th in the all-around behind Alina Harnasko, she qualified in all 4 apparatus finals.

On June 24–27, Ashirbayeva competed at the 2017 Asian Championships where she finished a disappointing 5th place in the all-around behind Japan's Sumire Kita.