Many potassium channels show voltage-dependent gating without a dedicated voltage sensor domain. This is not fully understood yet, but often explained by voltage-induced changes of ion occupation in the five distinct K+ binding sites in the selectivity filter. To better understand this mechanism of filter gating we measured the single-channel current and the rate constant of sub-millisecond channel closure of the viral K+ channel KcvNTS for a wide range of voltages and symmetric and asymmetric K+ concentrations in planar lipid membranes. A model-based analysis employed a global fit of all experimental data, i.e., using a common set of parameters for current and channel closure under all conditions. Three different established models of ion permeation and various relationships between ion occupation and gating were tested. Only one of the models described the data adequately. It revealed that the most extracellular binding site (S0) in the selectivity filter functions as the voltage sensor for the rate constant of channel closure. The ion occupation outside of S0 modulates its dependence on K+ concentration. The analysis uncovers an important role of changes in protein flexibility in mediating the effect from the sensor to the gate.