  We consider discrete $\beta$-ensembles as introduced by Borodin, Gorin and
Guionnet in (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017).
Under general assumptions, we establish a large deviation principle for their
rightmost particle. We apply our general results to two classes of measures
that are related to Jack symmetric functions.
