Between 2006 and 2010, while Professor of Music at Gresham College, London, Parker presented four series of free public lectures, one example being "Verdi and Milan" in 2007 which is available on video.
[2] In addition to teaching, Parker has been active as joint editor in the preparation of critical editions of the work of 19th-century Italian composer Gaetano Donizetti for the Milan publishing house Ricordi.
For ten years he was founding co-editor (with Arthur Groos) of the Cambridge Opera Journal, and he continues as General Editor of The Critical Edition of the Operas of Gaetano Donizetti published it Italy by Casa Ricordi of Milan and in the United States by the University of Chicago Press under the auspices of the Fondazione Donizetti.
Additionally, along with Dotto, he has co-authored the critical edition of Lucia di Lammermoor which was presented at the Royal Opera House, London in 2003.
[14] He received the "Premio Giuseppe Verdi" in 1986, was a Guggenheim Fellow in 1986–87, and in 1991 was awarded the Dent Medal of the Royal Musical Association.