Characterizing the galaxy population in the early Universe holds the key to understanding the evolution of these objects and the role they played in cosmic reionization. However, the number of observations at the very highest redshifts are to date, few. In order to shed light on the properties of galaxies in the high-redshift Universe and their interstellar media, we observe the Lyman-$alpha$ emitting galaxy z7_GSD_3811 at $z=7.664$ with band 6 and 8 at the Atacama Large Millimeter/submillimeter Array (ALMA). We target the far-infrared [O III] 88 $mu m$, [C II] 158 $mu m$ emission lines and dust continuum in the star-forming galaxy z7_GSD_3811 with ALMA. We combine these measurements with earlier observations in the rest-frame ultraviolet (UV) in order to characterize the object, and compare results to those of earlier studies observing [O III] and [C II] emission in high-redshift galaxies. The [O III] 88 $mu m$ and [C II] 158 $mu m$ emission lines are undetected at the position of z7_GSD_3811, with $3sigma$ upper limits of $1.6 times 10^{8} L_{odot}$ and $4.0 times 10^{7} L_{odot}$, respectively. We do not detect any dust continuum in band 6 nor band 8. The measured rms in the band 8 and band 6 continuum is 26 and 9.9 $mu Jy beam^{-1}$, respectively. Similar to several other high-redshift galaxies, z7_GSD_3811 exhibits low [C II] emission for its star formation rate compared to local galaxies. Furthermore, our upper limit on the [O III] line luminosity is lower than all the previously observed [O III] lines in high-redshift galaxies with similar ultraviolet luminosities. Our ALMA band 6 and 8 dust continuum observations imply that z7_GSD_3811 likely has a low dust content, and our non-detections of the [O III] and [C II] lines could indicate that z7_GSD_3811 has a low metallicity ($Z lesssim 0.1 Z_{odot}$).
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