  Addressing the discrepancy between the late and early time measurements of
the Hubble parameter, $H_0$, and the so-called $S_8$ parameter has been a
challenge in precision cosmology. Several models are present to address these
tensions, but very few of them can do so simultaneously. In the past, we have
suggested Banks-Zaks/Unparticles as an emergent Dark Energy model and claimed
that it can ameliorate the Hubble tension. In this work, we test this claim and
perform a likelihood analysis of the model and its parameters are given current
data and compare it to $\Lambda$CDM. The model offers a possible resolution of
Hubble tension and softens the Large Scale Structure (LSS) tension without
employing a scalar field or modifying the gravitational sector. Our analysis
shows a higher value of $H_0 \sim 70 - 73$ km/sec/Mpc and a slightly lower
value of $S_8$ for various combinations of data sets. Consideration of Planck
CMB data combined with the Pantheon sample and SH0ES priors lowers the $H_0$
and $S_8$ tension to $0.96 \sigma$ and $0.94 \sigma$ respectively with best-fit
$\Delta \chi^2 \approx -10$ restoring cosmological concordance. Significant
improvement in the likelihood persists for other combinations of data sets as
well. Evidence for the model is given by inferring one of its parameters to be
$x_0\simeq-4.36$.
