We describe the computation of charged lepton flavour violating processes such as $\mu \to e \gamma$, $\mu \to 3e$ and Muon conversion in the vicinity of nuclei in a fully realistic Pati-Salam (PS) model with gauged flavour symmetry. Our model combines PS and flavour symmetries in a renormalisable framework, which additionally includes realistic masses and mixing angles for the quark and lepton sector. PS Scalar fields in the adjoint representation break dynamically via their vacuum expectation values the PS gauge group and generate different flavour structures for up-type quarks, down-type quarks and leptons. Due to the mixture of new heavy fermions with the Standard model fermions sizeable tree-level flavour violating interactions are generated. We apply the current and future limits for charged lepton flavour violating processes to the predictions of our model.