This paper presents a search for a new $Z^\prime$ resonance decaying into a pair of dark quarks which hadronise into dark hadrons before promptly decaying back to Standard Model particles. This analysis is based on proton-proton collision data recorded at $\sqrt{s}=13$ TeV with the ATLAS detector at the Large Hadron Collider between 2015 and 2018, corresponding to an integrated luminosity of 139 fb$^{-1}$. After selecting events containing large-radius jets with high track multiplicity, the invariant mass distribution of the two leading jets is scanned to look for an excess above a data-driven estimate of the Standard Model multi-jet background. No significant excess of events is observed and the results are thus used to set $95 \%$ confidence-level upper limits on the production cross-section times branching ratio of the $Z^\prime$ to dark quarks as a function of the $Z^\prime$ mass for various dark-quark scenarios.
