  We examine further the ability of the New Early Dark Energy model (NEDE) to
resolve the current tension between the Cosmic Microwave Background (CMB) and
local measurements of $H_0$ and the consequences for inflation. We perform new
Bayesian analyses, including the current datasets from the ground-based CMB
telescopes Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT),
and the BICEP/Keck telescopes, employing an updated likelihood for the local
measurements coming from the S$H_0$ES collaboration. Using the S$H_0$ES prior
on $H_0$, the combined analysis with Baryonic Acoustic Oscillations (BAO),
Pantheon, Planck and ACT improves the best-fit by $\Delta\chi^2 = -15.9$ with
respect to $\Lambda$CDM, favors a non-zero fractional contribution of NEDE,
$f_{\rm NEDE} > 0$, by $4.8\sigma$, and gives a best-fit value for the Hubble
constant of $H_0 = 72.09$ km/s/Mpc (mean $71.48_{-0.81}^{+0.79}$ with $68\%$
C.L.). A similar analysis using SPT instead of ACT yields consistent results
with a $\Delta \chi^2 = - 23.1$ over $\Lambda$CDM, a preference for non-zero
$f_{\rm NEDE}$ of $4.7\sigma$ and a best-fit value of $H_0=71.77$ km/s/Mpc
(mean $71.43_{-0.84}^{+0.84}$ with $68\%$ C.L.). We also provide the
constraints on the inflation parameters $r$ and $n_s$ coming from NEDE,
including the BICEP/Keck 2018 data, and show that the allowed upper value on
the tensor-scalar ratio is consistent with the $\Lambda$CDM bound, but, as also
originally found, with a more blue scalar spectrum implying that the simplest
curvaton model is now favored over the Starobinsky inflation model.
