  Quasar proximity zones at $z>5.5$ correspond to over-dense and over-ionized
environments. Galaxies found inside proximity zones can therefore display
features which would otherwise be masked by absorption in the IGM. We
demonstrate the utility of this quasar-galaxy synergy by reporting the
discovery of the first three `proximate Lyman-$\alpha$ emitters' (LAEs) within
the proximity zone of quasar J0836 at $z=5.802$ (\textit{Aerith A, B} and
\textit{C}). \textit{Aerith A}, located behind the quasar with an impact
parameter $D_\perp = 278$ pkpc, provides the first detection of a
Lyman-$\alpha$ transverse proximity effect. We model the transmission and show
it constrains the onset of J0836's quasar phase to $0.2
\text{Myr}<t<20\text{Myr}$ in the past. The second object, \textit{Aerith B} at
a distance $D=750$ pkpc from the quasar, displays a bright, broad double-peaked
\lal emission line. Based on relations calibrated at $z\leq3$, the peak
separation implies a low ionizing $f_{\text{esc}} \lesssim 1\%$, the most
direct such constraint on a reionization-era galaxy. We fit the Ly-$\alpha$
line with an outflowing shell model, finding a completely typical central
density $\text{log N}_{\text{HI}}/\text{cm}^{-2} = 19.3_{-0.2}^{+0.8}$, outflow
velocity $v=16_{-11}^{+4}$ km s$^{-1}$, and gas temperature $\text{log}
T/\text{K} = 3.8_{-0.7}^{+0.8}$ compared to $2<z<3$ analogue LAEs. Finally, we
detect an emission line at $\lambda=8177$ \AA\ in object \textit{Aerith C}
which, if it is \lal at $z=5.726$, would correspond closely with the end of the
quasar's proximity zone ($\Delta z<0.02$ from the boundary) and suggests the
quasar influences the IGM up to $\sim85$ cMpc away, making it the largest
quasar proximity zone. Via the analyses conducted here, we illustrate how
proximate LAEs offer unique insight into the ionizing properties of both
quasars and galaxies during the epoch of reionization.
