There's that whole "New York Tenor" school - Liebman, Grossman, Brecker, Berg, Mintzer. This in a parallell to the whole "Brothers" school of Lester Young disciples of a few years earlier. In fact, I once drew a cartoon of Prez greeting Trane at the Pearly Gates, extending his hand and saying, "You too?". Nobody I showed it to got the joke...
Historically, the biggest non-African-American contributions to jazz have come from Jewish-Americans & Italiain-Americans. Why that is probably as much sociological as musicological, but Dan Morgenstern, in the notes to a Sonny Berman Onyx LP entitled, iirc, SOME BEAUTIFUL JEWISH MUSIC, went into a bit of commentary about the similarity between the melismatic, "wailing" quality of certain cantorial (NOT Eddie! ) traditions and jazz. Pretty interesting stuff.
And speaking of Ziggy Ellman, is it "common knowledge" that his classic solo bit on Goodman's "And The Angels Sing" was based on a traditional Jewish dance/rhythm? Sorry, I don't remember exactly which, but it was called a fralich or something like that. Again, sorry I don't know the exact name. I'd be more than glad to be enlightened, however. Whatever, it was an early (and overt) use of what I guess could be called "Klezmer" elements in a "mainstream" setting.