The following is something I wrote in a Facebook group in response to a clarinetist wanting to test the jazz waters for the first time:
Part of what will help getting started with playing jazz is gaining an understanding of the role of the clarinet in jazz, from a chronological standpoint. In traditional jazz, the role of the clarinet was ornamental: it outlined the harmony by arpeggiating the chords around the cornet melody, typically in the upper register.
Start with some earlier recordings of players like Johnny Dodds and Sidney Bechet. Play along with the recordings and see if you can pick up some of their licks by ear and execute them. Record yourself while you are doing this and listen critically to your performance. Then progress to the next generation of players like Benny Goodman, Barney Bigard, Pee Wee Russell, Artie Shaw, and Stan Hasselgard. You will see that some of their improvisational devices are a clear evolution of the idiomatic devices of the previous generation of clarinetists. When you have absorbed enough of their playing, you should be ready for more modern players like Buddy DeFranco, Eddie Daniels, and Ken Peplowski, and you’ll understand both what is idiomatic to the clarinet in jazz as well as how the modern vocabulary developed.
Remember, jazz is traditionally an aural art, and prior to the advent of formal jazz education, players learned by emulating their favorite musicians. As a novice improvisor, you will learn far more at this stage of the game by playing along with recordings and analyzing what your favorite players are doing rather than using publications. Books are valuable and have their place, but ultimately, your ear will be the best arbiter, so as a fledgling jazz musician, it is imperative that you develop that part of your arsenal before incorporating theory into the equation.