  An amplitude analysis of flavour-untagged $B_s^0 \to J/\psi p \bar{p}$ decays
is performed using a sample of $797\pm31$ decays reconstructed with the LHCb
detector. The data, collected in proton-proton collisions between 2011 and
2018, correspond to an integrated luminosity of 9 $\text{fb}^{-1}$. Evidence
for a new structure in the $J/\psi p$ and $J/\psi \bar{p}$ systems with a mass
of $4337 \ ^{+7}_{-4} \ ^{+2}_{-2}~\text{MeV}$ and a width of $29 \
^{+26}_{-12} \ ^{+14}_{-14}~\text{MeV}$ is found, where the first uncertainty
is statistical and the second systematic, with a significance in the range of
3.1 to 3.7 $\sigma$, depending on the assigned $J^P$ hypothesis.
