Data in B-meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of D( s ) mesons which originate from c→ dℓ¯ νl and c→ sℓ¯ νℓ charged-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements | Vcd| and | Vcs| of the Cabibbo–Kobayashi–Maskawa matrix and extract them from the D( s ) decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic D(s)+→e+νe modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.