  Axions provide a natural and well-motivated dark matter candidate, with the
capability to convert directly to photons in the presence of an electromagnetic
field. A particularly compelling observational target is the conversion of dark
matter axions into photons in the magnetospheres of highly magnetised neutron
stars, which is expected to produce a narrow spectral peak centred at the
frequency of the axion mass. We point the MeerKAT radio telescope towards the
isolated neutron star J0806.4$-$4123 for $10$-hours of observation and obtain
the radio spectra in the frequency range $769$-$1051$ MHz. By modelling the
conversion process of infalling axion dark matter (DM), we then compare these
spectra to theoretical expectations for a given choice of axion parameters.
Whilst finding no signal above $5\sigma$ in the data, we provide a unique
constraint on the Primakoff coupling of axion DM, $g_{{\rm
a}\gamma\gamma}\lesssim 9.3 \times 10^{-12}\,{\rm GeV}^{-1}$ at the $95\%$
confidence level, in the mass range $3.18$-$4.35\,\mu$eV. This result serves
the strongest constraint in the axion mass range $4.20$-$4.35\,\mu$eV.
