An amplitude analysis of flavour-untagged $B_s^0 to J/psi p bar{p}$ decays is performed using a sample of $797pm31$ 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.