Pictures show klezmer bands from the 1890s-1930s in Eastern Europe with a poyk un tastsn (bass drum of varying size with a cymbal attached), or a hand-held frame drum (with or without jingles). It seems that the role of drummer was often given to a young member of the band as part of their training.
In the USA, drum kits became part of the standard line-up as the slower dances and music for listening fell out of favour.
Good klezmer drummers 'play the melody', even as they provide rhythmic accompaniment.
Simon Roth's short introduction packs in a lot of information. Take a look!
Klezmer drummers in the late 19th and earlier 20th centuries included:
Eastern Europe / USA Jake Silber
USA Irving Gratz, Jacob Hoffman (also xylophone), Julie Epstein
Klezmer drummers in the later 20th century and today include:
Canada Lorie Wolf
Germany Hampus Melin, Thilo Jörgl
Japan Miwazow Kogure
Russia Evgeny Lizin (also tsimbl)
UK Guy Schalom, Simon Roth
USA Aaron Alexander, David Licht, Elaine Hoffman-Watts, Eve Sicular, Richie Barshay