Experimental data on rare $B$-meson decays indicate deviations from Standard Model predictions. In studies of these decays, new sources of CP violation are often neglected. We discuss CP violation in the rare $B$-meson decays $B\to K\ell^+\ell^- (\ell = \mu,e)$ and point to two phenomena that arise when new sources of CP violation are included. First, the Wilson coefficients $C_{9\ell}$ and $C_{10\ell}$ become complex, and we show how we can extract their values from measurements of direct and mixing-induced CP asymmetries. Second, new sources of CP violation can generate nontrivial lepton flavour universality violation. Such violation is usually measured through ratios like $R_K$ and $R_{K^*}$, but we show that measuring only these ratios leaves a large parameter space unexplored. These results bring exciting opportunities to reveal New Physics effects in the high-precision era.