Abstract Pair instability (PI) and pulsational PI prevent the formation of black holes (BHs) with mass ${\gtrsim}\,\, 60$ M⊙ from single star evolution. Here, we investigate the possibility that BHs with mass in the PI gap form via stellar mergers and multiple stellar mergers, facilitated by dynamical encounters in young star clusters. We analyze 104 simulations, run with the direct N-body code nbody6++gpu coupled with the population synthesis code mobse. We find that up to ∼6 % of all simulated BHs have mass in the PI gap, depending on progenitor’s metallicity. This formation channel is strongly suppressed in metal-rich (Z = 0.02) star clusters, because of stellar winds. BHs with mass in the PI gap are initially single BHs but can efficiently acquire companions through dynamical exchanges. We find that ∼21%, 10% and 0.5% of all binary BHs have at least one component in the PI mass gap at metallicity Z = 0.0002, 0.002 and 0.02, respectively. Based on the evolution of the cosmic star formation rate and metallicity, and under the assumption that all stars form in young star clusters, we predict that ∼5 % of all binary BH mergers detectable by advanced LIGO and Virgo at their design sensitivity have at least one component in the PI mass gap.