  Theoretical models of protoplanetary disc dispersal predict a phase where
photoevaporation has truncated the disc at several AU, creating a pressure trap
which is dust-rich. Previous models predicted this phase could be long-lived
(~Myr), contrary to the observational constraints. We show that dust in the
pressure trap can be removed from the disc by radiation pressure exerting a
significant acceleration, and hence radial velocity, on small dust particles
that reside in the surface layers of the disc. The dust in the pressure trap is
not subject to radial drift so it can grow to reach sizes large enough to
fragment. Hence small particles removed from the surface layers are replaced by
the fragments of larger particles. This link means radiation pressure can
deplete the dust at all particle sizes. Through a combination of 1D and 2D
models, along with secular models that follow the disc's long-term evolution,
we show that radiation pressure can deplete dust from pressure traps created by
photoevaporation in ~1e5 years, while the photoevaporation created cavity still
resides at 10s of AU. After this phase of radiation pressure removal of dust,
the disc is gas-rich and dust depleted and radially optically thin to stellar
light, having observational signatures similar to a gas-rich, young debris
disc. Indeed many of the young stars (~<10 Myr old) classified as hosting a
debris disc may rather be discs that have undergone this process.
