  Thermodynamic uncertainty relations have emerged as universal bounds on
current fluctuations in non-equilibrium systems. Here we derive a new bound for
a particular class of run-and-tumble type processes using the mathematical
framework of renewal-reward theory which can be applied to both Markovian and
non-Markovian systems. We demonstrate the results for selected single-particle
models as well as a variant of the asymmetric simple exclusion process with
collective tumbles. Our bound is relatively tight for a broad parameter regime
and only requires knowledge of the statistics of run lengths and the mean
entropy production rate of tumbles.
