We present new , high-angular resolution interferometric observations with the Karl G. Jansky Very Large Array of ^ { 12 } CO J = 1 - 0 line emission and 4 – 8 GHz continuum emission in the strongly lensed , z = 2.3 submillimetre galaxy , SMM J21352-−0102 . Using these data , we identify and probe the conditions in \sim 100 pc clumps within this galaxy , which we consider to be potential giant molecular cloud complexes , containing up to half of the total molecular gas in this system . In combination with far-infrared and submillimetre data , we investigate the far-infrared/radio correlation , measuring q _ { IR } = 2.39 \pm 0.17 across SMM J21352 . We search for variations in the properties of the interstellar medium throughout the galaxy by measuring the spatially-resolved q _ { IR } and radio spectral index , \alpha _ { radio } , finding ranges q _ { IR } = [ 2.1 , 2.6 ] and \alpha _ { radio } = [ -1.5 , -0.7 ] . We argue that these ranges in \alpha _ { radio } and q _ { IR } may reflect variations in the age of the ISM material . Using multi- J ^ { 12 } CO data , we quantitatively test a recent theoretical model relating the star-formation rate surface density to the excitation of ^ { 12 } CO , finding good agreement between the model and the data . Lastly , we study the Schmidt-Kennicutt relation , both integrated across the system and within the individual clumps . We find small offsets between SMM J21352 and its clumps relative to other star-forming galaxy populations on the Schmidt-Kennicutt plot – such offsets have previously been interpreted as evidence for a bi-modal star-formation law , but we argue that they can be equally well explained as arising due to a combination of observational uncertainties and systematic biases in the choice of model used to interpret the data .