Low-frequency radio observations are revealing an increasing number of diffuse synchrotron sources from galaxy clusters, dominantly in the form of radio halos or radio relics. The existence of this diffuse synchrotron emission indicates the presence of relativistic particles and magnetic fields. It is still an open question what mechanisms exactly are responsible for the population of relativistic electrons driving this synchrotron emission. The LOFAR Two-metre Sky Survey Deep Fields offer a unique view of this problem. Reaching noise levels below 30 $mu$Jy/beam, these are the deepest images made at the low frequency of 144 MHz. This paper presents a search for diffuse emission in galaxy clusters in the first data release of the LOFAR Deep Fields. We detect a new high-redshift radio halo with a flux density of $8.9 pm 1.0$ mJy and corresponding luminosity of $P_{144mathrm{MHz}}=(3.6 pm 0.6)times10^{25}$ W Hz$^{-1}$ in an X-ray detected cluster at $z=0.77$ with a mass estimate of $M_{500} = 3.3_{-1.7}^{+1.1} times 10^{14} M_odot.$ Deep upper limits are placed on clusters with non-detections. We compare the results to the correlation between halo luminosity and cluster mass derived for radio halos found in the literature. This study is one of few to find diffuse emission in low mass ($M_{500} < 5times10^{14} M_odot$) systems and shows that deep low-frequency observations of galaxy clusters are fundamental for opening up a new part of parameter space in the study of non-thermal phenomena in galaxy clusters.
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