He is the Composer-in-Residence for the Armenian State Symphony Orchestra, and an associate composer at the Yehudi Menuhin School.

One day his friend, viola player David Aaron Carpenter saw one of his scores on Alexey's desk.

[4] Alexey's works have been showcased in concert venues such as the Wiener Musikverein, Berlin Philharmonie, Carnegie Hall, the Kennedy Center in Washington, D.C.,[5] The Concertgebouw in Amsterdam, Munich's Gasteig, London's Wigmore Hall, Rome's Teatro Argentina, among others.

The overture to his ballet, “Crystal Palace,” was performed at the 40th Gramophone Classical Music Awards event in London.

[8] Shor's works have been performed by many soloists and ensembles, such as (in alphabetical order) Behzod Abduraimov, Salvatore Accardo, Ray Chen, Steven Isserlis, Clara-Jumi Kang, Evgeny Kissin, Denis Kozukhin, Shlomo Mintz, Mikhail Pletnev, Gil Shaham, Yeol Eum Son, Yekwon Sunwoo, Maxim Vengerov, Nikolaj Znaider and many others.