  PSR B1820$-$30A is located in the globular cluster NGC 6624 and is the
closest known pulsar to the centre of any globular cluster. We present more
than 25 years of high-precision timing observations of this millisecond pulsar
and obtain four rotational frequency time derivative measurements. Modelling
these higher-order derivatives as being due to orbital motion, we find
solutions which indicate that the pulsar is in either a low-eccentricity
($0.33\lesssim e\lesssim0.4$) smaller orbit with a low mass companion (such as
a main sequence star, white dwarf, neutron star, or stellar mass black hole) or
a high-eccentricity ($e\gtrsim0.9$) larger orbit with a massive companion. The
cluster mass properties and the observed properties of 4U 1820$-$30 and the
other pulsars in the cluster argue against the low-eccentricity possibility.
The high-eccentricity solution reveals that the pulsar is most likely orbiting
around an intermediate-mass black hole (IMBH) of mass $> 7,500$~M$_\odot$
located at the cluster centre. A gravitational model for the globular cluster,
which includes such a central black hole (BH), predicts an acceleration that is
commensurate with that measured for the pulsar. It further predicts that the
model-dependent minimum mass of the IMBH is $\sim60,000$~M$_\odot$. Accounting
for the associated contribution to the observed period derivative indicates
that the $\gamma$-ray efficiency of the pulsar should be between 0.08 and 0.2.
Our results suggest that other globular clusters may also contain central black
holes and they may be revealed by the study of new pulsars found sufficiently
close to their centres.
  Note that we found an erratum in Section 5 and thus, the
$\sim$60,000~M$_\odot$ mass mentioned above has to be replaced by the correct
model-dependent mass limit of $\sim$20,000~M$_\odot$. See the erratum appended.
