In an embodiment, a processor includes multiple domains including a core domain having at least one core to execute instructions and a graphics domain including at least one graphics engine to perform graphics operations and a power controller to control power consumption of the processor. The power controller may include a logic to receive an indication of a priority domain of the domains and to dynamically allocate power to the domains based on a power limit, one or more maximum domain frequency requests, and the priority domain indication. Other embodiments are described and claimed.