We present a flavour non-universal extension of the Standard Model combined with the idea of Higgs compositeness. At the TeV scale, the gauge groups SU(2)R and U(1)B−L are assumed to act in a non-universal manner on light- and third-generation fermions, while the Higgs emerges as a pseudo Nambu-Goldstone boson of the spontaneous global symmetry breaking Sp(4) → SU(2)L × \( \textrm{SU}{(2)}_R^{\left[3\right]} \) , attributed to new strong dynamics. The flavour deconstruction means the couplings of the light families to the composite sector (and therefore the pNGB Higgs) are suppressed by powers of a heavy mass scale (from which the Higgs is nevertheless shielded by compositeness), explaining the flavour puzzle. We present a detailed analysis of the radiatively generated Higgs potential, showing how this intrinsically-flavoured framework has the ingredients to justify the unavoidable tuning in the Higgs potential necessary to separate electroweak and composite scales. This happens for large enough values of the \( \textrm{SU}{(2)}_R^{\left[3\right]} \) gauge coupling and light enough flavoured gauge bosons resulting from the deconstruction, whose phenomenology is also investigated. The model is compatible with current experimental bounds and predicts new states at the TeV scale, which are within the reach of near future experimental searches.
