  In a series of previous papers, we have presented a new approach, based on
perturbative QCD, for the evolution of a jet in a dense quark-gluon plasma. In
the original formulation, the plasma was assumed to be homogeneous and static.
In this work, we extend our description and its Monte Carlo implementation to a
plasma obeying Bjorken longitudinal expansion. Our key observation is that the
factorisation between vacuum-like and medium-induced emissions, derived in the
static case, still holds for an expanding medium, albeit with modified rates
for medium-induced emissions and transverse momentum broadening, and with a
modified phase-space for vacuum-like emissions. We highlight a scaling relation
valid for the energy spectrum of medium-induced emissions, through which the
case of an expanding medium is mapped onto an effective static medium. We find
that scaling violations due to vacuum-like emissions and transverse momentum
broadening are numerically small. Our new predictions for the nuclear
modification factor for jets $R_{AA}$, the in-medium fragmentation functions,
and substructure distributions are very similar to our previous estimates for a
static medium, maintaining the overall good qualitative agreement with existing
LHC measurements. In the case of $R_{AA}$, we find that the agreement with the
data is significantly improved at large transverse momenta $p_T\gtrsim 500$ GeV
after including the effects of the nuclear parton distribution functions.
