The ice pack in the Arctic Ocean averages only about 5 m thick and floats on the Arctic Ocean. Because it is not in contact with the seafloor (and never has been), it does not exert force on the Earth's crust. Thus, although melting of the ice pack is of considerable climatic and environmental concern, it will have no effect on plate motions or the frequency of earthquakes.
Catastrophic melt of the Greenland ice sheet is another matter. The Greenland ice sheet is up to nearly 3 km thick and exerts considerable downward pressure on the the land on which it rests. If this ice sheet were to substantially melt, it is possible that more earthquakes might occur in Greenland; plate motions, however, would continue, as they had prior to the melting.
If the IPCC forecast of several degrees increase in average global temperature by the end of the century proves to be correct, the Greenland Ice Sheet is likely to shrink considerably, driving sea level higher. Although IPCC has forecast little or no contribution of this ice sheet to sea level rise by the end of the century, it may be underestimating the problem. Some scientists are raising alarms about the health of the Greenland Ice Sheet due to warming of the past few decades.