  We study a novel interacting dark energy $-$ dark matter scenario where the
anisotropic stress of the large scale inhomogeneities is considered. The dark
energy has a constant equation of state and the interaction model produces
stable perturbations. The resulting picture is constrained using different
astronomical data aiming to measure the impact of the anisotropic stress on the
cosmological parameters. Our analyses show that a non-zero interaction in the
dark sector is allowed while a non-interaction scenario is recovered within
68\% CL. The anisotropic stress is also constrained to be small, and its zero
value is permitted within 68\% CL. The dark energy equation of state, $w_x$, is
also found to be close to `$-1$' boundary. However, from the ratio of the CMB
TT spectra, we see that the model has a mild deviation from the $\Lambda$CDM
cosmology while such deviation is almost forbidden from the CMB TT spectra
alone. Although the deviation is not much significant, but from the present
data, we cannot exclude such deviation. Overall, at the background level, the
model is close to the $\Lambda$CDM cosmology while at the level of
perturbations, a non-zero but a very small interaction in the dark sector is
permitted. Perhaps, a more accurate conclusion can be made with the next
generation of surveys. We also found that the region $w_x < -1$, is found to be
effective to release the tension on $H_0$. Finally, from the Bayesian analysis,
we find that $\Lambda$CDM remains in still preferred over the interacting
scenarios.
