  In the present work, newly developed microscopic effective $sd$-valence shell
interactions such as chiral next-to-next-to-next-to-leading order (N3LO),
$J$-matrix inverse scattering potential (JISP16), Daejeon16 (DJ16), and
monopole-modified DJ16 (DJ16A) are employed to study the nuclear structural
properties of sulphur, chlorine, and argon isotopes with $N \geq Z$. These
interactions are derived using the \textit{ab initio} no-core shell-model and
the OLS unitary transformation method. We calculate energy spectra and
electromagnetic properties to test the predictive strength of the effective
interactions for these heavier $sd$-shell nuclei. For a complete systematic
study, we compare the microscopic results with the phenomenological USDB
results and experimental data. By looking at the excitation energies of these
nuclei, the DJ16A interaction is found to be {the} most suitable for these
$sd$-shell nuclei among all microscopic interactions. The electric quadrupole
transition strength and excitation energy of the first $2^+$ state data of
even-even sulphur isotopes indicate the presence of the $N=20$ shell closure.
Quadrupole moment predictions are also made using these interactions where
experimental data are unknown. Magnetic moments are in excellent agreement with
the experimental values. The root-mean-square deviations are also calculated to
provide an idea of how accurate the interactions are.
