Regarding early 20th century clarinet performance history, particularly those who frequented New York, there are many significant clarinetists who come to mind.

Benny Goodman (1909-86), Frederick Thurston (1939-2017), Eduard Brunner (1939-2017), and Dieter Klöcker (1936-2011) were all accredited with expanding repertoire. Charles Draper (1869-1952), Reginald Kell (1906-81), Simeon Bellison (1883-1954), Louis Cahuzac (1880-1960), Gervase de Peyer (1926-2017) were known for producing significant recordings. 

This excerpt from the Cambridge Companion to the Clarinet includes a fun anecdote about jazzman and clarinetist Benny Goodman:

One of the earliest works to combine jazz with the classical idiom was Gershwin’s Rhapsody in Blue (1924). The opening glissando – not In Gershwin’s original score but interpolated as a joke by Paul White- man’s clarinetist Ross Gorman – made the composer famous overnight. This glissando is not every classical player’s cup of tea, and indeed proved fatal to Baltimore’s principal clarinet, Georges Grisez (1884-1946), who died on stage after performing it. To jazzman Benny Goodman (1909-86) it held no terrors and the story goes that, on walking into NBC studios one day in 1942 to record with his group and finding the stage set for a rehearsal of Rhapsody, he demanded of the doorman: ‘How can they possibly do that without me?’ Word spread and he was engaged by Toscanini. Goodman has had a profound intluence on twentieth-century classical music for the clarinet through commissions offered to leading composers of the day. He had had a classical training himself before entering the world of jazz and when, having sat atop that world for some time, he gave his first commission he was already a millionaire.