  The mergers of two neutron stars are typically accompanied by broad-band
electromagnetic emission from either a relativistic jet or a kilonova. It has
also been long predicted that coherent radio emission will occur during the
merger phase or from a newly formed neutron star remnant, however this emission
has not been seen to date. This paper presents the deepest limits for this
emission from a neutron star merger folowing triggered LOFAR observations of
the short gamma-ray burst (SGRB) 181123B, starting 4.4 minutes after the GRB
occurred. During the X-ray plateau phase, a signature of ongoing energy
injection, we detect no radio emission to a 3$\sigma$ limit of 153 mJy at 144
MHz (image integration time of 136 seconds), which is significantly fainter
than the predicted emission from a standard neutron star. At a redshift of 1.8,
this corresponds to a luminosity of $2.5 \times 10^{44}$ erg s$^{-1}$. Snapshot
images were made of the radio observation on a range of timescales, targeting
short duration radio flashes similar to fast radio bursts (FRBs). No emission
was detected in the snapshot images at the location of GRB 181123B enabling
constraints to be placed on the prompt coherent radio emission model and
emission predicted to occur when a neutron star collapses to form a black hole.
At the putative host redshift of 1.8 for GRB 181123B, the non detection of the
prompt radio emission is two orders of magnitude lower than expected for
magnetic reconnection models for prompt GRB emission and no magnetar emission
is expected.
