  The James Webb Space Telescope (JWST) has uncovered a ubiquitous population
of dust-obscured compact sources at $z\gtrsim 4$. Many of these objects exhibit
signs of active galactic nucleus (AGN) activity, making their study crucial for
understanding the formation of supermassive black holes (SMBHs) and their
growth with host galaxies. In this work, we examine low and medium resolution
JWST/NIRSpec spectra from the JADES GTO public data release in the GOODS-N
field of a red, luminous ($M_{\rm B}\sim-22.2$ mag) and compact ($<500$ pc)
source at $z=4.13$. The rest-optical ($\lambda_{\rm rest} > 4000$ A) continuum
of this source is strongly dominated by a massive (log$_{10}$[$M_*/M_\odot]
\sim 10.6$), quenched (log$_{10}$[sSFR/yr$^{-1}$] $< -11$) galaxy, as indicated
by the clear presence of a Balmer break and stellar absorption lines.
Star-formation history modeling reveals a starburst episode followed by rapid
quenching about 200 Myr ago. The spectrum shows extremely broad (FWHM $\sim
2500$ km/s) H$\alpha$ emission and elevated optical line ratios, indicating an
actively accreting SMBH. Moreover, our work has potentially revealed clear AGN
signatures in the rest-UV in LRDs for the first time, via a detection of a
strong Ly$\alpha$ emission and a broad MgII, doublet. The derived black hole
mass of log$_{10}$($M_{\rm BH}/M_\odot) \sim 7.3$ results in $M_{\rm
BH}/M_*\sim 0.04$ %, consistent with the local relations, unlike the elevated
ratios in other high-$z$ reddened AGN. Finally, we use JWST data from AGN at
$z=4-10$ to explore an evolutionary link between high-$z$ reddened AGN, early
quiescent galaxies, and local ellipticals.
