  We investigate the effect on the entanglement dynamics of an impurity moving
at constant velocity in a closed quantum system. We focus on one-dimensional
strongly-correlated lattice models, both in the presence of integrable and
chaotic dynamics. In the former, the slow impurity is preceded by fast
quasiparticles carrying an "endogenous" entanglement front which decays in time
as a power-law; on the contrary, a fast impurity drags itself an "exogenous"
entanglement front which never fades. We argue that these effects are valid for
generic systems whose correlations propagate inside a light-cone. To assess the
fully chaotic regime, we formulate a random circuit model which supports a
moving impurity and a sharp lightcone. Although the qualitative behavior is
similar to the integrable case, the endogenous regime is only visible at short
times due to the onset of diffusive energy transport. Our predictions are
supported by numerical simulations in the different regimes.
