[abbreviated] We present a census of Lyalpha emission at $zgtrsim7$ utilizing deep near infrared HST grism spectroscopy from the first six completed clusters of the Grism Lens-Amplified Survey from Space (GLASS). In 24/159 photometrically selected galaxies we detect emission lines consistent with Lyalpha in the GLASS spectra. Based on the distribution of signal-to-noise ratios and on simulations we expect the completeness and the purity of the sample to be 40-100% and 60-90%, respectively. For the objects without detected emission lines we show that the observed (not corrected for lensing magnification) 1$sigma$ flux limits reaches $5times10^{-18}$erg/s/cm$^{2}$ per position angle over the full wavelength range of GLASS (0.8-1.7$mu$m). Based on the conditional probability of Lyalpha emission measured from the ground at $zsim7$ we would have expected 12-18 Lyalpha emitters. This is consistent with the number of detections, within the uncertainties, confirming the drop in Lyalpha emission with respect to $zsim6$. These candidates include a promising source at $z=8.1$. The spatial extent of Lyalpha in a deep stack of the most convincing Lyalpha emitters with $langle zrangle=7.2$ is consistent with that of the rest-frame UV continuum. Extended Ly$alpha$ emission, if present, has a surface brightness below our detection limit, consistent with the properties of lower redshift comparison samples. From the stack we estimate upper limits on rest-frame UV emission line ratios and find $f_textrm{CIV} / f_textrm{Ly${alpha}$} lesssim 0.32$ and $f_textrm{CIII]} / f_textrm{Ly$alpha$} lesssim 0.23$ in good agreement with other values published in the literature.
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