The discovery of RNA enzymes, ribozymes, provided strong support to the RNA world hypothesis suggesting that early life evolved from RNAs able to both store genetic information and catalyze biochemical reactions. Moreover, evidence is accumulating that primitive life might have emerged in deep-sea environments and, thus, at high hydrostatic pressures. If true, ribozymes should be able to function under those pressures. In this work, we ask if and possibly how ribozymes could function at high pressures. To this end, we specifically focus on the chemical reaction steps of the self-cleavage catalysis of hairpin ribozyme by employing extensive QM/MM metadynamics simulations. We find that the reaction scenario at high pressures is vastly different than that at ambient conditions, yet the rate-limiting reaction barrier and, thus, the reaction rate are only marginally affected. Therefore, the results indeed suggest that ribozymes would function at high pressures but by following a vastly different reaction scenario.