In an embodiment, a processor has a core to execute instructions which includes a first cache memory, a clock generation logic to receive and distribute a first clock signal to a plurality of units of the core, and a core activity monitor logic to monitor activity of the core and, responsive to a miss in the first cache memory, to send a first restriction command to cause the clock generation logic to reduce delivery of the first clock signal to at least one of the units to a first frequency less than a frequency of the first clock signal. Other embodiments are described and claimed.