Gleeson studied Piano and Timpani & Percussion at the Royal Academy of Music, London, and Composition and Film Scoring at the University of California at Los Angeles (UCLA).

[10] (Gleeson also studied Voice periodically with the famed Irish vocal teacher Veronica Dunne at the Dublin Institute of Technology Conservatory of Music & Drama.

In December 1989, Gleeson moved to Los Angeles, left the world of the freelance orchestral musician, and directed his time exclusively to conducting and composition.

Gleeson conducted the premier CD recording of Tchaikovsky's Ode to Joy,[11] The original Romeo and Juliet Fantasy Overture and Prokofiev's Zdravitsa with the London Philharmonic Orchestra and Choir.

In January 2016 Gleeson lead the Dublin Philharmonic Orchestra on its second tour of China, performing in Suzhou, Wuhan, Tianjin, Harbin and Changsha.

Founder and Director of Ireland's "MA in Scoring for Film & Visual Media", a Pulse College/Windmill Lane Studios/Dublin Institute of Technology collaboration.