Reionization is an inhomogeneous process, thought to begin in small ionized bubbles of the intergalactic medium (IGM) around overdense regions of galaxies. Recent Ly{alpha} studies during the epoch of reionization show 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 Deep Imaging Multi-Object Spectrograph and MOSFIRE data set from the Texas Spectroscopic Search for Ly{alpha} Emission at the End of Reionization Survey. We constrain the Ly{alpha} equivalent width (EW) distribution at 6.0<z<8.2, which is described by an exponential form, dN/dEW{prop.to}exp(-EW)/W_0_, with the characteristic e-folding scale width (W_0_). We confirm a significant drop in the Ly{alpha} strength (i.e., W_0_) at z>6. Furthermore, we compare the redshift evolution of W0 between galaxies at different UV luminosities. UV-bright (M_UV_<-21 [i.e., L_UV_>L*]) galaxies show weaker evolution with a decrease of 0.4(+/-0.2) dex in W_0_ at z>6, while UV-faint (M_UV_>-21 [_LUV_<L*]) galaxies exhibit a significant drop of 0.7-0.8(+/-0.2) dex in W_0_ from z<6 to z>6. If the change in W_0_ is proportional to the change in the IGM transmission for Ly{alpha} photons, then this is evidence that the transmission is "boosted" around UV-brighter galaxies, suggesting that reionization proceeds faster in regions around such galaxies.