  A new generation of radio telescopes with excellent sensitivity,
instantaneous {\it uv} coverage, and large fields of view, are providing
unprecedented opportunities for performing commensal transient searches. Here
we present such a commensal search in deep observations of short gamma-ray
burst fields carried out with the MeerKAT radio telescope in South Africa at
1.3 GHz. These four hour observations of eight different fields span survey
lengths of weeks to months. We also carry out transient searches in time slices
of the full observations, at timescales of 15 minutes, and 8 seconds. We find
122 variable sources on the long timescales, of which 52 are likely active
galactic nuclei, but there are likely also some radio flaring stars. While the
variability is intrinsic in at least two cases, most of it is consistent with
interstellar scintillation. In this study, we also place constraints on
transient rates based on state-of-the-art transient simulations codes. We place
an upper limit of $2\times10^{-4}$ transients per day per square degree for
transients with peak flux of 5 mJy, and an upper limit of $2.5\times10^{-2}$
transients per day per square degree for transients with a fluence of 10 Jy ms,
the minimum detectable fluence of our survey.
