  Clusters of topologically connected calorimeter cells around cells with large
absolute signal-to-noise ratio (topo-clusters) are the basis for calorimeter
signal reconstruction in the ATLAS experiment. Topological cell clustering has
proven performant in LHC Runs 1 and 2. It is, however, susceptible to
out-of-time pile-up of signals from soft collisions outside the 25 ns
proton-bunch-crossing window associated with the event's hard collision. To
reduce this effect, a calorimeter-cell timing criterion was added to the
signal-to-noise ratio requirement in the clustering algorithm. Multiple
versions of this criterion were tested by reconstructing hadronic signals in
simulated events and Run 2 ATLAS data. The preferred version is found to reduce
the out-of-time pile-up jet multiplicity by $\sim$50% for jet $p_\text{T}\sim
20$ GeV and by $\sim$80% for jet $p_\text{T} \gtrsim 50$ GeV, while not
disrupting the reconstruction of hadronic signals of interest, and improving
the jet energy resolution by up to 5% for $20 < p_\text{T} < 30$ GeV. Pile-up
is also suppressed for other physics objects based on topo-clusters (electrons,
photons, $\tau$-leptons), reducing the overall event size on disk by about 6%
in early Run 3 pile-up conditions. Offline reconstruction for Run 3 includes
the timing requirement.
