After a 30-year career as a classical saxophonist, he has in recent years turned more to conducting.
Kelly is artistic director of the Arcos Chamber Orchestra , which he co-founded in 2005.
He has lectured and served as a guest professor in London, The Hague, Hamburg, Düsseldorf, Helsinki, Rochester, Stuttgart, Lyon, Oslo, York, and other cities, and has published articles concerning aesthetics, contemporary music and the saxophone.
Kelly has performed as a soloist with many leading orchestras including the Stockholm Philharmonic, Helsinki Philharmonic, Berliner Staatskapelle, Deutsches Sinfonieorchester, Symphony Orchestra of the Bavarian Radio, Munich Philharmonic, Munich Chamber Orchestra, Radio-Sinfonie-Orchester Stuttgart, Gewandhaus-Orchester, Rotterdam Chamber Orchestra, Swedish Radio Orchestra, Finnish Radio Symphony Orchestra, Dresdner Staatskapelle, Ostrobothnian Chamber Orchestra, Swedish Chamber Orchestra, Residentie Orkest, Polish Chamber Orchestra, Orchester der Beethoven-Halle Bonn and Radio Philharmonisch Orkest (Holland).
Kelly has given the first performances of more than 200 works for saxophone, including 30 concertos for saxophone and orchestra. His performing repertoire consists primarily of works written expressly for him.
In 1995 he played the world premiere of Dimitri Terzakis's saxophone concerto, which was broadcast live to 27 nations.
Composers who have written works for Kelly include: Samuel Adler, Kalevi Aho, Osvaldas Balakauskas, Jürg Baur, Erik Bergman, David Blake, John Boda, Herbert Callhoff, Michael Denhoff, Violeta Dinescu, Brian Elias, Anders Eliasson, Werner Wolf Glaser, Sampo Haapamäki, Ingvar Karkoff, Maurice Karkoff, Tristan Keuris, Hans Kox, Nicola LeFanu, Otmar Mácha, Tera de Marez-Oyens, Miklós Maros, Gérard Masson, Roland Leistner-Mayer, Krzysztof Meyer, Gráinne Mulvey, Pehr-Henrik Nordgren, Enrique Raxach, Uros Rojko, Jan Sandström, Sven-David Sandström, Leif Segerstam, Manfred Stahnke, Dimitri Terzakis, Stefan Thomas, Friedrich Voss, and Iannis Xenakis
His recordings include:
Kelly authored a pamphlet titled "The Acoustics of the Saxophone from a Phenomenological Perspective" which is offered for sale on his web site.