  We present a deep survey of the SuperCLASS super-cluster - a region of sky
known to contain five Abell clusters at redshift $z\sim0.2$ - performed using
the Arcminute Microkelvin Imager (AMI) Large Array (LA) at 15.5$~$GHz. Our
survey covers an area of approximately 0.9 square degrees. We achieve a nominal
sensitivity of $32.0~\mu$Jy beam$^{-1}$ toward the field centre, finding 80
sources above a $5\sigma$ threshold. We derive the radio colour-colour
distribution for sources common to three surveys that cover the field and
identify three sources with strongly curved spectra - a high-frequency-peaked
source and two GHz-peaked-spectrum sources. The differential source count (i)
agrees well with previous deep radio source count, (ii) exhibits no evidence of
an emerging population of star-forming galaxies, down to a limit of 0.24$~$mJy,
and (iii) disagrees with some models of the 15$~$GHz source population.
However, our source count is in agreement with recent work that provides an
analytical correction to the source count from the SKADS Simulated Sky,
supporting the suggestion that this discrepancy is caused by an abundance of
flat-spectrum galaxy cores as-yet not included in source population models.
