Accumulating evidence suggests that glacier basal motion can produce seismogenic stick-slip events caused by frictional resistance at the ice-bed interface. Frequent and subsequent failure of multiple stick-slip patches may constitute sliding tremor in seismic recordings. We show that during stick-slip tremor at the base of an Alpine glacier, the released seismic moment increases by an order of magnitude. The tremor emerges during melt-intensive days and is associated with water pressure peaks in a nearby subglacial channel. We propose an extended slider-block model that explains the regular occurrence of stick-slip tremor by coupling seismically sliding patches to surrounding aseismically sliding bed regions. The model predicts that the stick-slip patches control the movement of their surrounding smoothly sliding bed regions via elastic coupling and stress transfer. Thus, tremor producing stick-slip patches could affect large-scale ice flow to a degree, which is underestimated in models, with implications on sea level rise projections.