We present a deep survey of the SuperCLASS super-cluster - a region of sky known to contain five Abell clusters at redshift $z\sim 0.2$ - performed using the Arcminute Microkelvin Imager (AMI) Large Array (LA) at 15.5$$GHz. Our survey covers an area of approximately 0.9 square degrees. We achieve a nominal sensitivity of $32.0 \mu$Jy beam$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ toward the field centre, finding 80 sources above a $5\sigma$ threshold. We derive the radio colour-colour distribution for sources common to three surveys that cover the field and identify three sources with strongly curved spectra - a high-frequency-peaked source and two GHz-peaked-spectrum sources. The differential source count (i) agrees well with previous deep radio source count, (ii) exhibits no evidence of an emerging population of star-forming galaxies, down to a limit of 0.24$$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.