Recently the RBC-UKQCD lattice collaboration presented new results for the hadronic matrix elements relevant for the ratio $varepsilon/varepsilon$ in the Standard Model (SM). With the present knowledge of the Wilson coefficients and isospin breaking effects there is still much room for new physics (NP) contributions to $varepsilon/varepsilon$ which could both enhance or suppress this ratio to agree with the data. The new SM value for the $K^0-bar K^0$ mass difference $Delta M_K$ from RBC-UKQCD is on the other hand by $2sigma$ above the data hinting for NP required to suppress $Delta M_K$. Simultaneously the most recent results for $K^+rightarrowpi^+ ubar u$ from NA62 and for $K_{L}rightarrowpi^0 ubar u$ from KOTO still allow for significant NP contributions. We point out that the suppression of $Delta M_K$ by NP requires the presence of new CP-violating phases with interesting implications for $Ktopi ubar u$, $K_Stomu^+mu^-$ and $K_Ltopi^0ell^+ell^-$ decays. Considering a $Z^prime$-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on $varepsilon/varepsilon$. The NP QCD penguin scenario for $varepsilon/varepsilon$ is excluded by SMEFT renormalization group effects in $varepsilon_K$ so that NP effects in $varepsilon/varepsilon$ are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy $Z^prime$ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM $Z$-boson. The outcome turns out to be very interesting.
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