  We present a model which employs $CP\times Z_3$ symmetries where quark mixing
and charged leptons masses are explained by following some texture. To achieve
neutrino mass and mixing, we write a non-renormalizable Lagrangian using
type-II seesaw mechanism by assuming ${\mathcal{O}}(1)$ couplings predicting no
$CP$ violation. Then, we calculate the value of the couplings for both normal
and inverted ordering of neutrino masses. We propose a mechanism of
ultra-violet (UV) completion that motivates the higher dimensional Lagrangian
in the neutrino sector. We also calculate the branching fraction of lepton
flavor violating decays driven by triplet scalar for the model. Later, it is
shown that the model can also accommodate maximal $CP$ violation by breaking
the $CP$ symmetry spontaneously.
