  Hypervelocity stars (HVSs) represent a unique population of stars in the
Galaxy reflecting properties of the whole Galactic potential. Determining their
origin is of fundamental importance to constrain the shape and mass of the dark
halo. The leading scenario for the ejection of HVSs is an encounter with the
supermassive black hole in the Galactic Centre. However, new proper motions
from the \textit{Gaia} mission indicate that only the fastest HVSs can be
traced back to the Galactic centre and the remaining stars originate in the
disc or halo. In this paper, we study HVSs generated by encounters of stellar
binaries with an intermediate-mass black hole (IMBH) in the core of a star
cluster. For the first time, we model the effect of the cluster orbit in the
Galactic potential on the observable properties of the ejected population. HVSs
generated by this mechanism do not travel on radial orbits consistent with a
Galactic centre origin, but rather point back to their parent cluster, thus
providing observational evidence for the presence of an IMBH. We also model the
ejection of high-velocity stars from the Galactic population of globular
clusters, assuming that they all contain an IMBH, including the effects of the
cluster's orbit and propagation of the star in the Galactic potential up to
detection. We find that high-velocity stars ejected by IMBHs have distinctive
distributions in velocity, Galactocentric distance and Galactic latitude, which
can be used to distinguish them from runaway stars and stars ejected from the
Galactic Centre.
