Awarded bronze medals in Ljubljana, Slovenia and Aichi, Japan, he finished as the third alternate for a place at the JGP Final.

Making his senior international debut, he placed tenth at the 2014 Golden Spin of Zagreb, an ISU Challenger Series event.

Placing sixth in the short program and first in the free skate, he won the gold medal by a margin of 5.32 points ahead of Latvia's Deniss Vasiļjevs.

He then took gold in Linz, Austria, with a total score 14 points higher than silver medalist Vincent Zhou, and qualified for the Junior Grand Prix Final.

Competing on the senior level, Aliev was awarded bronze at the 2015 International Cup of Nice and silver at the 2015 CS Tallinn Trophy.

In December, he won the silver medal at the 2015–16 JGP Final in Barcelona, having finished second to Nathan Chen of the United States.

Later that month, he placed sixth at the 2016 Russian Championships in Yekaterinburg before winning his first junior national title in January in Chelyabinsk.

He was awarded a small gold medal for his short program result at the 2016 World Junior Championships in Debrecen, Hungary.

Starting his season on the Junior Grand Prix series, Aliev won gold in Ostrava, Czech Republic, after placing first in both segments.

He ranked first in the short program, third in the free skate, and second overall in Taipei, Taiwan, winning the silver medal behind American Vincent Zhou and ahead of the teammate Alexander Samarin.

Competing at the 2019 Russian Championships, Aliev had a disastrous short program, falling on an underrotated quad toe loop and completely missing the takeoff on his planned triple Axel.

At his first Grand Prix event, 2019 Skate America, Aliev placed second in the short program, behind Nathan Chen and fractions of a point ahead of Keegan Messing.

[17] He was second in the free skate as well, barely back of the lead, and missed taking the gold medal due to repeating too many jumps and getting his final triple Lutz invalidated for violating the Zayak rule.

[21] Second in the free skate despite two falls, one on a quad toe loop and the other during his step sequence, Aliev captured his first Russian national title.

[27] With the pandemic continuing to affect international travel, the ISU opted to run the Grand Prix based primarily on geographic location.

[30] Aliev was chosen for the 2021 Channel One Trophy, a televised team event organized in lieu of the cancelled European Championships.

[37] His first Grand Prix assignment was initially the 2021 Cup of China, but following its cancellation he was reassigned to the 2021 Gran Premio d'Italia in Turin.