The growing appeal of carbon nanotube composites in the contemporary market derives from their exceptional thermal and chemical stability, coupled with electrical conductivity. In this study, we combined these salient features with a biobased epoxy matrix having vitrimeric properties, hence being reprocessable and resheapable, to obtain a biobased conductive coating. Epoxidised castor oil (ECO) was chosen as a monomer precursor for the straightforward synthesis. The synthesis relied on a cationic UV-curing process, embedding the conductive carbon nanotubes in the matrix. Photo DSC and transmission FTIR analysis were conducted to determine the final conversion of the epoxy rings in the cationic photocuring process. Thermo-mechanical properties were evaluated by tensile tests, and DMTA. Thermal stability was assessed by TGA. Dielectric spectroscopy confirmed increased electrical conductivity in the presence of increasing CNT content, reaching a percolation threshold at 0.5 phr of CNTs. Vitrimeric properties were proved by stress relaxation experiments, and the UV-cured composite underwent a thermo-activated transesterification reaction starting from 70 °C, catalysed by dibutyl phosphate. Overall, the ECO-CNT composite showed high thermal resistance (up to 400 °C) electrical conductivity with 0.5 phr CNT concentration, and vitrimeric properties. The study can be, therefore, considered a promising starting point to obtain sustainable biobased and electrically conductive vitrimers.