  We apply a recently developed theory for metastability in open quantum
systems to a one-dimensional dissipative quantum Ising model. Earlier results
suggest this model features either a non-equilibrium phase transition or a
smooth but sharp crossover, where the stationary state changes from
paramagnetic to ferromagnetic, accompanied by strongly intermittent emission
dynamics characteristic of first-order coexistence between dynamical phases. We
show that for a range of parameters close to this transition/crossover point
the dynamics of the finite system displays pronounced metastability, i.e., the
system relaxes first to long-lived metastable states, before eventual
relaxation to the true stationary state. From the spectral properties of the
quantum master operator we characterise the low-dimensional manifold of
metastable states, which are shown to be probability mixtures of two,
paramagnetic and ferromagnetic, metastable phases. We also show that for long
times the dynamics can be approximated by a classical stochastic dynamics
between the metastable phases that is directly related to the intermittent
dynamics observed in quantum trajectories and thus the dynamical phases.
