  Reionization is an inhomogeneous process, thought to begin in small ionized
bubbles of the intergalactic medium (IGM) around overdense regions of galaxies.
Recent Lyman-alpha (Ly$\alpha$) studies during the epoch of reionization show
growing evidence that ionized bubbles formed earlier around brighter galaxies,
suggesting higher IGM transmission of Ly$\alpha$ from these galaxies. We
investigate this problem using IR slitless spectroscopy from the Hubble Space
Telescope (HST) Wide-Field Camera 3 (WFC3) G102 grism observations of 148
galaxies selected via photometric redshifts at $6.0<z<8.2$. These galaxies have
spectra extracted from the CANDELS Ly$\alpha$ Emission at Reionization (CLEAR)
survey. We combine the CLEAR data for 275 galaxies with the Keck/DEIMOS+MOSFIRE
dataset from the Texas Spectroscopic Search for Ly$\alpha$ Emission at the End
of Reionization Survey. We then constrain the Ly$\alpha$ equivalent-width (EW)
distribution at $6.0<z<8.2$, which is described by an exponential form,
$dN/d\text{EW}\propto\text{exp(-EW)}/W_0$, with the characteristic $e$-folding
scale width ($W_0$). We confirm a significant drop of the Ly$\alpha$ strength
(or $W_0$) at $z>6$. Furthermore, we compare the redshift evolution of $W_0$
between galaxies at different UV luminosities. The UV-bright
($M_{\text{UV}}<-21$, or $L_{\text{UV}}>L^{*}$) galaxies show weaker evolution
with a decrease of 0.4 ($\pm$0.2) dex in $W_0$ at $z>6$ while UV-faint
($M_{\text{UV}}>-21$, or $L_{\text{UV}}<L^{*}$) galaxies exhibit a significant
drop by a factor of 0.7-0.8 ($\pm0.2$) dex in $W_0$ from $z<6$ to $z>6$. Our
results add to the accumulating evidence that UV-bright galaxies exhibit
boosted Ly$\alpha$ transmission in the IGM, suggesting that reionization
completes sooner in regions proximate to galaxies of higher UV luminosity.
