Na+/H+ antiporters exchange sodium ions and protons on opposite sides of lipid membranes. The electroneutral Na+/H+ antiporter NhaP from archaea Pyrococcus abyssi (PaNhaP) is a functional homolog of the human Na+/H+ exchanger NHE1, which is an important drug target. Here we resolve the Na+ and H+ transport cycle of PaNhaP by transition-path sampling. The resulting molecular dynamics trajectories of repeated ion transport events proceed without bias force, and overcome the enormous time-scale gap between seconds-scale ion exchange and microseconds simulations. The simulations reveal a hydrophobic gate to the extracellular side that opens and closes in response to the transporter domain motion. Weakening the gate by mutagenesis makes the transporter faster, suggesting that the gate balances competing demands of fidelity and efficiency. Transition-path sampling and a committor-based reaction coordinate optimization identify the essential motions and interactions that realize conformational alternation between the two access states in transporter function.