Recently, experiments have been testing
the neutral $D$ meson system with increasing precision. Since $D^0- \overline{D^0}$ mixing occurs through Flavour Changing Neutral Currents, Standard Model amplitudes are absent at the tree level and suppressed at the loop level. Therefore, heavy New Physics coupled to the up-type quarks could manifest itself by modifying the small charm mixing and CP-violating parameters.
We present a strategy to combine observables from the $D$ and $B$ meson systems within a Bayesian framework to determine simultaneously the charm mixing and CP-violating parameters and the CKM angle $\gamma$. We check consistency between $\gamma$ estimates obtained separating the beauty measurements according to the charge of the $B$ mesons. We obtain an updated determination of the dispersive and absorptive charm mixing parameters and the angle $\gamma$.